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AUG  18 


Conductivity  and  Viscosity  in 
Mixed  Solvents  Contain- 
ing Glycerol. 


DISSERTATION 


SUBMITTED  TO   THE    BOARD    OF   UNIVERSITY   STUDIES  OF 

THE   JOHNS   HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF    DOCTOR    OF    PHILOSOPHY 


BY 


MAURICE  ROLAND  SCHMIDT. 

/TIMORE. 


K^  JUNE,  1909. 


EASTON,  PA. 

ESCHENBACH  PRINTING  Co. 
1909. 


Conductivity  and  Viscosity  in 
Mixed  Solvents  Contain- 
ing Glycerol. 


DISSERTATION 


SUBMITTED  TO   THE    BOARD    OF   UNIVERSITY   STUDIES  OF 

THE    JOHNS   HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF    DOCTOR    OF    PHILOSOPHY 


BY 

MAURICE  ROLAND  SCHMIDT. 

BALTIMORE. 
JUNE,  1909. 


EASTON,  PA. 

ESCHENBACH  PRINTING  Co. 
1909. 


CONTENTS. 


Acknowledgment 4 

PART  I. 

Introduction 5 

Previous  Work  in  Nonaqueous  Solvents 5 

Mixed  Solvents 7 

Conductivity  and  Viscosity 7 

Experimental 8 

PART    II. 

Introduction 24 

Glycerol  as  a  Solvent 25 

Conductivity  Apparatus 26 

Solvents 27 

Solutions 29 

Viscosity 30 

Lithium  Bromide 34 

Cobalt  Chloride 45 

Potassium  Iodide 52 

Temperature  Coefficients  of  Conductivity 56 

Viscosity  and  Fluidity 59 

Summary  of  Facts  Established 63 

Biography 64 


228299 


ACKNOWLEDGMENT. 

The  author  wishes  here  to  thank  President  Remsen,  Pro- 
fessor Morse,  Professor  Jones,  Associate  Professor  Acree  and 
Professor  Mathews  for  valuable  instruction  in  both  lecture- 
room  and  laboratory. 

Special  thanks  are  due  to  Professor  Jones,  at  whose  sugges- 
tion and  under  whose  direction  this  investigation  was  carried 
out. 

The  author  feels  under  special  obligations  to  Professor 
Renouf  and  Dr.  Gilpin,  whose  kindly  interest  and  valuable 
advice  on  many  matters  have  been  of  the  greatest  assistance 
throughout  the  author's  connection  with  the  University. 


Conductivity  and  Viscosity  in 
Mixed  Solvents  Contain- 
ing GlyceroL 


PART  I. 

This  investigation  is  the  latest  in  a  series  which  has  been 
carried  out  in  the  Physical  Chemical  Laboratory  of  the  Johns 
Hopkins  University,  dealing  with  the  relations  between  elec- 
trical conductivity  and  viscosity  of  solutions  of  various  elec- 
trolytes in  certain  nonaqueous  solvents,  and  in  mixtures  of 
these  solvents  with  water  and  with  each  other.  The  results 
of  the  first  seven  investigations  have  been  published  as  Mono- 
graph No.  80,  of  the  Carnegie  Institution  of  Washington, 
1907.  Since  that  time  an  eighth  communication  by  Jones 
and  Veazey1  has  appeared,  and  a  ninth,  by  Jones  and  Mahin,2 
is  about  to  be  published.  It  now  seems  desirable  to  bring 
together  the  more  important  facts  thus  far  established  and 
the  conclusions  drawn  from  them. 

Previous  Work  in  Nonaqueous  Solvents. 
The  modern  theory  of  solutions  has  been  largely  based  on 

1  Z.  physik.  Chem.,  62,  44  (1908). 

2  To  appear  in  Z.  physik.  Chem.,  1909,  Jubelband  zu  Arrhenius. 


experimental  work  done  in  aqueous  solutions,  but  lately  an 
increasing  amount  of  attention  has  been  given  to  the  behavior 
of  solutions  in  solvents  other  than  water;  and  the  present 
work  has  to  deal  with  certain  questions  that  presented  them- 
selves in  connection  with  solutions  in  methyl  and  ethyl  alco- 
hols, acetone,  and  mixtures  of  these  solvents  with  water  and 
with  one  another. 

Considerable  work  had  already  been  done  on  solutions  in 
these  solvents,  and  a  few  measurements  had  been  made  of 
solutions  in  mixtures.  Carrara1  carried  out  an  extensive 
investigation,  using  methyl  alcohol  as  the  solvent,  and  study- 
ing the  electrical  conductivity  of  a  great  variety  of  salts. 
Zelinsky  and  Krapiwin2  also  worked  with  solutions  in  methyl 
alcohol,  and  with  a  few  in  a  mixture  of  methyl  alcohol  and 
water.  This  work  will  be  referred  to  again. 

Hartwig,3  Vicentini,4  Cattaneo,5  and  Vollmer8  have  de- 
termined the  conductivity  of  a  great  variety  of  salts  in  ethyl 
alcohol.  A  few  measurements  have  been  made  in  some  of 
the  higher  alcohols  by  Schlamp,7  Carrara,8  and  Kablukoff.0 
Cattaneo10  and  Carrara11  also  published  the  results  of  a  good 
deal  of  work  in  acetone.  The  work  of  Dutoit  and  Aston,12 
as  well  as  that  of  Dutoit  and  Friderich,13  should  be  mentioned 
here.  Dutoit  and  Aston  formulated  the  hypothesis  that  the 
dissociating  power  of  a  solvent  is  a  direct  function  of  its  degree 
of  association  in  the  pure  state.  This  relation  has  been  found 
to  hold  for  a  large  number  of  cases,  but  there  are  many  and 
important  exceptions  to  it,  and  its  value  has  often  been  over- 
estimated. 

By  far  the  largest  and  most  important  work  on  organic 

1  Gazz.  Chim.  Ital.,  26  [1],  119  (1896). 

2  Z.  physik.  Chem.,  21,  35  (1896). 

3  Wied.  Ann.,  33,  58  (1888);  43,  838  (1891). 
*  Beibl.  Wied.  Ann.,  9,  131  (1885). 

6  Ibid.,  18,  219,  365  (1894). 

6  Wied.  Ann.,  52,  328  (1894). 

7  Z.  physik.  Chem.,  14,  272  (1894). 

8  Gazz.  Chim.  Ital.,  27  [1],  221  (1897). 
8  Z.  physik.  Chem.,  4,  432  (1889). 

10  Rend.  R.  Accad.  Line.  [5],  4,  2  sem.,  63. 

11  Loc.  cit. 

"  Compt.  Rend.,  125,  240  (1897). 

»  Bull.  Soc.  Chim.  [3],  19,  321  (1897). 


solvents  is  the  series  of  investigations  carried  out  by  Walden 
and  his  students. 

Ten  papers1  have  appeared  from  his  laboratory,  dealing 
with  the  relations  between  conductivity  and  viscosity,  di- 
electric constants,  refractive  indices,  solvent  power,  etc., 
for  about  thirty  organic  solvents. 

Mixed  Solvents. 

Wakeman2  made  an  extensive  investigation  with  aqueous 
ethyl  alcohol,  finding  that  the  conductivity  of  organic  acids 
in  it  decreased  with  increasing  amounts  of  alcohol.  Zelinsky 
and  Krapiwin3  obtained  the  interesting  result  that  the  con- 
ductivity of  sodium  and  ammonium  bromides  and  iodides 
in  aqueous  methyl  alcohol  containing  50  per  cent  alcohol  is 
less  than  the  conductivity  in  either  the  alcohol  or  the  water. 
Wakeman  found  from  his  results  that  the  equation 

A 

=  constant 


—  />) 

held  satisfactorily  for  many  substances  in  mixtures  of  ethyl 
alcohol  and  water,  A  being  the  difference  between  the  con- 
ductivity of  the  electrolyte  in  water  and  in  the  mixture,  and 
p  the  percentage  of  alcohol  by  volume. 
Cohen4  found  the  relation 

—  constant 


A1 
ftz,  H2O.  Ale. 

to    hold    independently    of    temperature    and    concentration. 

Conductivity  and  Viscosity. 

Wiedemann5  was  the  first  to  point  out  a  connection  between 
conductivity  and  viscosity.  From  his  work  on  solutions  of 
copper  sulphate,  he  formulated  a  relation 

kv 

-f  =  constant, 

P 

1  Z.  physik.  Chem.,  46,  103;  54,  129;  55,  207;   55,  281.   683;   58,  479;   59,   192; 
59,385;  60,  87;  61,  633. 

2  Ibid.,  11,49  (1893). 

3  Loc.  cit. 

*  Z.  physik.  Chem.,  25,  31  (1898). 
5  Pogg.  Ann.,  99,  229  (1856). 


experimental  work  done  in  aqueous  solutions,  but  lately  an 
increasing  amount  of  attention  has  been  given  to  the  behavior 
of  solutions  in  solvents  other  than  water;  and  the  present 
work  has  to  deal  with  certain  questions  that  presented  them- 
selves in  connection  with  solutions  in  methyl  and  ethyl  alco- 
hols, acetone,  and  mixtures  of  these  solvents  with  water  and 
with  one  another. 

Considerable  work  had  already  been  done  on  solutions  in 
these  solvents,  and  a  few  measurements  had  been  made  of 
solutions  in  mixtures.  Carrara1  carried  out  an  extensive 
investigation,  using  methyl  alcohol  as  the  solvent,  and  study- 
ing the  electrical  conductivity  of  a  great  variety  of  salts. 
Zelinsky  and  Krapiwin2  also  worked  with  solutions  in  methyl 
alcohol,  and  with  a  few  in  a  mixture  of  methyl  alcohol  and 
water.  This  work  will  be  referred  to  again. 

Hartwig,3  Vicentini,4  Cattaneo,5  and  Vollmer6  have  de- 
termined the  conductivity  of  a  great  variety  of  salts  in  ethyl 
alcohol.  A  few  measurements  have  been  made  in  some  of 
the  higher  alcohols  by  Schlamp,7  Carrara,8  and  Kablukoff.0 
Cattaneo10  and  Carrara11  also  published  the  results  of  a  good 
deal  of  work  in  acetone.  The  work  of  Dutoit  and  Aston,12 
as  well  as  that  of  Dutoit  and  Friderich,13  should  be  mentioned 
here.  Dutoit  and  Aston  formulated  the  hypothesis  that  the 
dissociating  power  of  a  solvent  is  a  direct  function  of  its  degree 
of  association  in  the  pure  state.  This  relation  has  been  found 
to  hold  for  a  large  number  of  cases,  but  there  are  many  and 
important  exceptions  to  it,  and  its  value  has  often  been  over- 
estimated. 

By  far  the  largest  and  most  important  work  on  organic 

1  Gazz.  Chim.  Ital.,  26  [1],  119  (1896). 

2  Z.  physik.  Chem.,  21,  35  (1896). 

3  Wied.  Ann.,  33,  58  (1888);  43,  838  (1891). 
*  Beibl.  Wied.  Ann.,  9,  131  (1885). 

6  Ibid.,  18,  219,  365  (1894). 

6  Wied.  Ann.,  52,  328  (1894). 

7  Z.  physik.  Chem.,  14,  272  (1894). 

8  Gazz.  Chim.  Ital.,  27  [1],  221  (1897). 

9  Z.  physik.  Chem.,  4,  432  (1889). 

10  Rend.  R.  Accad.  Line.  [5],  4,  2  sem.,  63. 

11  Loc.  cit. 

J2  Compt.  Rend.,  125,  240  (1897). 

18  Bull.  Soc.  Chim.  [3],  19,  321  (1897). 


solvents  is  the  series  of  investigations  carried  out  by  Walden 
and  his  students. 

Ten  papers1  have  appeared  from  his  laboratory,  dealing 
with  the  relations  between  conductivity  and  viscosity,  di- 
electric constants,  refractive  indices,  solvent  power,  etc., 
for  about  thirty  organic  solvents. 

Mixed  Solvents. 

Wakeman2  made  an  extensive  investigation  with  aqueous 
ethyl  alcohol,  finding  that  the  conductivity  of  organic  acids 
in  it  decreased  with  increasing  amounts  of  alcohol.  Zelinsky 
and  Krapiwin3  obtained  the  interesting  result  that  the  con- 
ductivity of  sodium  and  ammonium  bromides  and  iodides 
in  aqueous  methyl  alcohol  containing  50  per  cent  alcohol  is 
less  than  the  conductivity  in  either  the  alcohol  or  the  water. 
Wakeman  found  from  his  results  that  the  equation 


— r  =  constant 
-p} 

held  satisfactorily  for  many  substances  in  mixtures  of  ethyl 
alcohol  and  water,   A  being  the  difference  between  the  con- 
ductivity of  the  electrolyte  in  water  and  in  the  mixture,  and 
p  the  percentage  of  alcohol  by  volume. 
Cohen4  found  the  relation 

.-: —  =  constant 
>.  Ale. 

to    hold   independently    of    temperature    and    concentration. 

Conductivity  and  Viscosity. 

Wiedemann5  was  the  first  to  point  out  a  connection  between 
conductivity  and  viscosity.  From  his  work  on  solutions  of 
copper  sulphate,  he  formulated  a  relation 

ky 

~£>  =  constant, 

P 

1  Z.  physik.  Chem.,  46,  103;  54,  129;  55,  207;   55,  281,   683;   58,  479;   59,   192; 
59,385;  60,  87;  61,  633. 

2  Ibid.,  11,  49  (1893). 

3  Loc.  cit. 

*  Z.  physik.  Chem.,  25,  31  (1898). 
5  Pogg.  Ann.,  99,  229  (1856). 


8 

where  k  is  the  conductivity  of  a  solution  of  concentration  p, 
and  y  is  its  viscosity. 

Stephan1  showed  that  in  alcohol  and  water  mixtures  the 
temperature  coefficients  of  conductivity  and  fluidity  were 
nearly  the  same.  He  also  found  a  minimum  conductivity 
in  certain  mixtures. 

For  a  complete  discussion  of  the  electrochemistry  of  non- 
aqueous  solutions,  one  should  consult  Carrara's  "Elettro- 
chimica  delle  soluzioni  non  aquose"2  which  covers  the  litera- 
ture well  up  to  the  year  1906. 

Experimental. 

The  work  of  Jones  and  his  assistants  comprises  a  uniform 
series  of  investigations,  the  same  experimental  methods  being 
used  in  each.  The  conductivities  were  determined  by  the 
ordinary  Kohlrausch  method.  The  bridge  wire,  resistance 
boxes,  thermometers,  etc.,  were  all  calibrated  or  tested  against 
the  same  standard  instruments.  Measurements  were  made 
at  two  temperatures,  o°  and  25°. 

The  conductivity  water  was  purified  by  the  method  of 
Jones  and  Mackay,3  and  had  a  mean  conductivity  at  o°  of 
i  X  io~6,  and  twice  that  amount  at  25°.  The  alcohols  were 
purified  by  careful  distillations  after  being  boiled  with  lime 
several  times.  The  conductivity  of  the  ethyl  alcohol  was 
between  0.2  X  lo"6  and  2  X  icf6,  and  that  of  the  methyl 
alcohol  was  about  the  same  as  that  of  the  water.  The  acetone 
was  dried  by  calcium  chloride,  and  had  an  average  conduc- 
tivity of  about  0.6  X  lo""6. 

Viscosity  measurements  were  made  by  means  of  the  Ost- 
wald  viscometer.4 

The  work  of  Thorpe  and  Rodger5  was  consulted  for  the 
values  of  the  viscosity  of  water  at  o°  and  25°. 

The  standard  of  conductivity  is,  in  all  cases,  that  of  a  fiftieth- 
normal  solution  of  potassium  chloride  at  25°,  which  is  taken 
as  129.7  reciprocal  Siemens' s  units. 

i  Wied.  Ann.,  17,  673  (1883). 

2Gazz.  Chim.  Ital.,  37  [1],  1  (1907);  Ahrens'  Sammlung,  12,  11  (1908). 

3  Am.  Chem.  Journ.,  19,  91  (1897). 

4  Phys.-chem.  Mess.,  2nd.  Ed.,  p.  260. 
8  Phil.  Trans.,  185,  A,  307  (1894). 


Jones  and  Lindsay  undertook  a  further  investigation  of 
the  phenomenon  observed  by  Zelinsky  and  Krapiwin,  and 
by  Cohen,  namely,  a  minimum  value  of  conductivity  in  a 
fifty  per  cent  mixture  of  methyl  alcohol  and  water.  The 
solvents  used  were  methyl,  ethyl,  and  w-propyl  alcohols, 
water,  and  binary  mixtures  of  these  liquids.  The  electrolytes 
studied  were  potassium,  cadmium,  and  strontium  iodides, 
ammonium  bromide,  and  lithium  nitrate.  In  every  case  it 
was  found  that  the  molecular  conductivity  of  solutions  in 
the  mixed  solvents  was  less  than  the  average  calculated  from 
the  conductivities  in  the  components.  In  some  cases,  curves 
with  well-defined  minima  were  obtained  at  o°,  some  of  which 
persisted  at  25°,  while  others  developed  into  sagging  curves 
with  no  minima. 

As  a  partial  explanation  of  these  facts,  this  tentative  sug- 
gestion was  made: 

It  is  known  that  water  and  the  alcohols  are  highly  asso- 
ciated substances,  that  is,  their  molecules  in  the  liquid  state 
exist  as  complexes,  the  composition  of  which  varies  with  the 
temperature.  Now,  according  to  the  hypothesis  of  Dutoit 
and  Aston,  only  those  substances  which  are  associated  can 
dissociate  molecules.  Hence,  water  and  the  alcohols,  on 
coming  in  contact,  lower  the  state  of  association  of  each  other, 
until  a  condition  of  equilibrium  is  reached.  The  mixture, 
being  now  less  associated  than  its  components,  should  have 
less  dissociating  power  than  the  latter,  and  this  is  actually 
the  case  in  every  instance  studied.  Moreover,  the  lowering 
of  conductivity  is  more  marked  when  the  alcohols  are  mixed 
with  water  than  when  they  are  mixed  with  each  other,  be- 
cause they  are  associated  to  a  less  degree  than  water. 

This  conclusion  was  subsequently  confirmed  by  Jones  and 
Murray.1  By  means  of  cryoscopic  measurements  with  water, 
formic  and  acetic  acids,  and  mixtures  of  these  liquids,  they 
showed  that  the  molecular  weights  of  these  substances  were 
always  less,  even  in  very  concentrated  solutions,  than  the 
values  obtained  by  Ramsay  and  Shields,  who  had  found  that 
these  liquids  are  all  highly  associated  in  the  pure  condition. 

1  Am.  Chem.  Journ.,  30,  193  (1903). 


10 

Jones  and  Carroll1  extended  the  work  of  Jones  and  Lindsay. 
The  solvents  used  were  water,  methyl  and  ethyl  alcohols, 
and  various  mixtures  of  these  with  one  another.  The  elec- 
trolytes chosen  were  cadmium  iodide,  sodium  iodide,  calcium 
nitrate,  hydrochloric  acid,  sodium  acetate,  and  potassium 
iodide.  Cadmium  iodide  in  mixtures  of  methyl  alcohol  and 
water  showed  no  minimum,  except  in  the  curves  for  V  =  16, 
V  —  32,  and  V  =  64  at  o°.  Here  a  minimum  appeared  in 
the  75  per  cent  mixture.  In  all  cases,  however,  the  conduc- 
tivities were  less  than  the  average  values.  In  mixtures  of 
ethyl  alcohol  and  water,  the  same  salt  showed  entirely  similar 
phenomena,  though  no  minima  were  observed.  Sodium 
iodide  gave  a  well-defined  minimum  in  the  50  per  cent  mixture 
of  methyl  alcohol  and  water.  Calcium  nitrate  in  the  same 
solvents  gave  no  minimum,  while  the  conductivities  again 
did  not  obey  the  law  of  averages.  Hydrochloric  acid  gave 
irregular  results,  but  a  minimum  was  noticed  in  a  mixture  con- 
taining 90  per  cent  methyl  alcohol.  Sodium  acetate  in  various 
mixtures  of  acetic  acid  and  water  gave  entirely  irregular 
figures. 

An  effort  was  made  to  determine  the  dissociating  power 
of  the  methyl  alcohol-water  mixtures,  since  it  had  been  no- 
ticed that  the  molecular  conductivity,  pv,  for  hydrochloric 
acid  became  constant  at  rather  small  dilutions  in  these  solvents. 
Limiting  values  of  conductivity  were  obtained  for  sodium, 
potassium,  and  ammonium  iodides  and  bromides,  and  lithium 
nitrate,  in  50  per  cent  methyl  alcohol.  In  all  these  cases, 
the  dissociation  was  complete  in  the  mixture  at  a  dilution 
considerably  less  than  that  necessary  for  complete  dissocia- 
tion in  water  or  methyl  alcohol.  It  now  remained  to  find 
the  cause  of  the  minimum. 

Two  factors  are  to  be  considered,  amount  of  dissociation, 
and  ionic  mobility.  The  first  has  been  eliminated,  hence  the 
minimum  must  be  caused  by  a  decrease  in  ionic  mobility. 
From  the  results  of  various  observers,  it  was  found  that  the 
viscosity  of  aqueous  alcohol  in  the  neighborhood  of  a  50  per 
cent  mixture  is  higher  than  that  of  either  of  its  constituents. 

1  Am.  Chem.  Journ.,  32,  521  (1904). 


II 

Furthermore,  the  change  in  viscosity  with  increasing  content 
of  alcohol  is  more  marked  at  low  temperatures  than  at  higher, 
and  rise  in  temperature  shifts  the  maximum  in  viscosity, 
or  minimum  in  fluidity,  slightly  towards  the  mixture  con- 
taining the  greater  percentage  of  alcohol.  These  phenomena 
are  closely  paralleled  by  the  conductivity  minima.  The 
latter  all  occur  in  or  near  the  50  per  cent  mixtures,  and  are 
more  marked  at  o°  than  at  25°.  Cadmium  iodide,  for  in- 
stance, shows  a  minimum  at  o°  in  three  solutions,  but  none 
at  25°.  Potassium  iodide,  strontium  iodide,  and  lithium 
nitrate  give  minima  in  the  50  per  cent  mixture  at  o°,  which 
move  to  the  75  per  cent  mixture  at  25°. 

A  method  was  then  devised  for  comparing  the  variations 
in  fluidity  and  conductivity,  and  for  studying  the  effect  on 
conductivity  of  changes  in  fluidity.  The  differences  between 
the  (calculated)  average  values  and  the  observed  conduc- 
tivities and  fluidities  in  the  various  mixtures  were  expressed 
in  percentages,  and  in  all  cases  the  variation  in  fluidity  was 
found  to  be  greater  than  the  variation  in  conductivity.  Letting 

A<£  and    Aw     represent   the   two  variations,  then 

hkcp 

represents  the  relative  effect  of  variation  in  fluidity  on  con- 
ductivity. If  the  two  effects  are  equal,  the  expression  be- 
comes equal  to  zero.  It  was  found  that  in  the  40  per  cent 
mixtures,  the  effect  of  change  in  fluidity  on  conductivity  is 
greatest.  Finally,  the  temperature  coefficients  of  conduc- 
tivity and  of  fluidity  were  not  found  to  differ  markedly;  in 

other  words,  ~~  is  nearly  a  constant. 

9 
Jones  and  Carroll  therefore  conclude  that  the  decrease  in 

conductivity  in  binary  mixtures  is  due  primarily  to  a  decrease 
in  the  fluidity  of  the  solvent,  and,  consequently,  a  decrease 
in  the  ionic  mobility,  and  secondarily  to  the  effect  of  one 
associated  solvent  on  the  association  of  another. 

A  quantitative  study  of  the  relation  between  the  conduc- 
tivity and  viscosity  of  different  solutions  was  then  made. 
In  order  that  data  for  different  solvents  might  be  comparable, 
measurements  were  made  with  "comparable  equivalent  solu- 


12 

tions,"  that  is,  solutions  containing  the  same  number  of  gram- 
molecules  of  electrolyte  in  the  same  number  of  gram-molecules 
of  solvents.  The  result  was  that  the  conductivities  of  such 
solutions  were  found  to  be  inversely  proportional  to  the  vis- 
cosity of  the  solvent,  and  directly  proportional  to  the  associa- 
tion factor  of  the  solvent,  or  to  the  amount  of  dissociation 
of  the  electrolyte  in  that  solvent.  Otherwise  expressed, 


=  constant  or  -      =  constant. 
x  a 

The  work  of  Bassett1  showed  that  silver  nitrate,  in  mix- 
tures of  methyl  alcohol  and  ethyl  alcohol  with  water,  presented 
phenomena  entirely  in  accord  with  the  observations 
of  Jones  and  Lindsay  and  of  Jones  and  Carroll. 
The  conductivity  curves  for  ethyl  alcohol-water  solu- 
tions fall  far  below  the  straight  line  of  averages,  but 
give  no  minima;  the  methyl  alcohol-water  curves,  on  the 
other  hand,  give  well-marked  minima  at  both  o°  and  25  °, 
the  variation  from  the  average  being  more  pronounced  at  the 
lower  temperature. 

Jones  and  Bingham2  introduced  another  solvent  into  the 
investigation,  namely,  acetone,.  The  electrolytes  studied  were 
lithium  nitrate,  potassium  iodide,  and  calcium  nitrate,  and 
quite  unexpected  results  were  obtained.  Lithium  nitrate, 
in  mixtures  of  acetone  and  water,  gave  curves  with  an  inflec- 
tion point  at  low  dilutions  and  at  o°,  which  developed  minima 
in  the  higher  dilutions  at  o°.  The  conductivity  curves  for 
solutions  in  mixtures  of  methyl  and  ethyl  alcohols  with  acetone 
gave  maxima,  which,  in  the  higher  dilutions,  occurred  always 
in  the  mixtures  containing  75  per  cent  acetone.  The  curves 
are  very  nearly  straight  lines  below  this  point,  but  drop  rapidly 
to  the  values  in  100  per  cent  acetone.  This  fact  is  important 
in  connection  with  the  work  of  Mahin,  to  be  considered  later. 
Potassium  iodide  in  mixtures  of  the  alcohols  with  acetone 
gave  conductivity  curves  which  were  very  nearly  straight 
lines,  either  slightly  convex  or  concave  towards  the  axis 
denoting  percentages  of  acetone.  In  mixtures  of  acetone 

1  Am.  Chem.  Journ.,  32,  409  (1904). 

2  Ibid.,  34,  481  (1905). 


13 

and  water,  the  same  salt  gave  pronounced  minima  in  the 
neighborhood  of  the  50  per  cent  mixtures.  Calcium  nitrate 
in  mixtures  of  methyl  and  ethyl  alcohols  with  acetone  gave 
curves  with  maxima  at  both  o°  and  25°.  In  mixtures  with 
water,  the  results  were  again  irregular.  In  the  first  place, 
the  values  of  jj.v  for  calcium  nitrate  in  acetone  are  surprisingly 
small,  less  than  those  for  lithium  nitrate  or  potassium  iodide, 
although  it  is  a  ternary  electrolyte.  In  consequence,  the 
curves  for  acetone-water  mixtures,  at  dilutions  greater  than 
V  =  400,  reach  a  minimum  in  the  50  per  cent  mixture,  and 
rise  to  the  75  per  cent  mixtures — in  this  point  resembling  the 
curves  for  potassium  iodide — but  thereafter  sink  to  the  small 
values  on  the  ordinate  representing  100  per  cent  acetone. 

The  viscosity  measurements  brought  to  light  the  facts  that 
the  fluidity  curves  of  mixtures  of  the  alcohols  with  acetone 
are  nearly  straight  lines,  while  the  acetone-water  mixtures 
give  a  minimum  fluidity  in  the  50  per  cent  mixture.  In 
general,  therefore,  the  relation  found  by  Jones  and  Carroll 
holds  for  mixtures  containing  acetone,  that  is,  there  exists 
a  parallelism  between  the  conductivity  and  fluidity  curves. 
However,  the  maximum  conductivity  obtained  with  solutions 
of  calcium  and  lithium  nitrates  in  mixtures  of  acetone  with 
the  alcohols  demands  explanation.  Two  possible  causes 
suggest  themselves  at  once. 

First,  there  may  be  an  increase  in  dissociation  in  the  75 
per  cent  mixtures,  where  the  maximum  occurs.  Secondly, 
there  may  be  an  increased  mobility  of  the  ions,  due  to  a  diminu- 
tion in  the  size  of  the  ionic  spheres.  The  idea  of  ionic  spheres, 
proposed  by  Kohlrausch  and  by  Jones,  postulates  the  exist- 
ence of  an  atmosphere  of  solvent  molecules  clustered  about 
the  ion.  To  decide  between  these  two  possibilities,  we  may 
first  consider  the  increase  in  dissociation.  The  fluidity  data 
show  that  the  acetone-alcohol  mixtures  are  not  more  associated 
than  the  pure  solvents;  hence,  using  Dutoit  and  Aston's 
hypothesis,  we  should  not  expect  to  find  greater  dissociation 
in  the  mixtures.  Moreover,  while  it  is  true  that  the  maximum 
conductivity  occurs  in  the  75  per  cent  mixture,  this  is  true 
only  for  dilute  solutions,  the  maximum  shifting  to  the  25 


14 

per  cent  mixture  as  the  concentration  increases.  This  would 
not  occur  if  the  75  per  cent  mixture  had  the  greatest  disso- 
ciating power.  Therefore,  the  tentative  view  is  accepted, 
that  the  maximum  in  conductivity  is  due  to  a  change  in  the 
dimensions  of  the  ionic  spheres,  and  a  consequent  increase 
in  migration  velocity. 

The  conclusion  of  Dutoit  and  Friderich,  and  of  Jones  and 
Carroll,  that  conductivity  is  proportional  to  dissociation  and 
inversely  proportional  to  viscosity,  must  be  supplemented 
by  taking  into  consideration  the  possible  changes  in  the  size 
of  the  ionic  spheres  of  solvent  molecules. 

Jones  and  Rouiller1  undertook  the  study  of  silver  nitrate. 
This  salt  gave  results  practically  identical  with  those  obtained 
by  Jones  and  Bingham  for  lithium  and  calcium  nitrates. 
The  conductivity  curves  for  acetone-water  mixtures  gave 
inflection  points  in  the  higher  concentrations,  and  a  pseudo- 
maximum  in  the  75  per  cent  mixture,  the  value  of  the  molecular 
conductivities  declining  rapidly,  however,  to  the  figures  for 
pure  acetone.  The  curves  for  mixtures  of  methyl  and  ethyl 
alcohols  are  nearly  straight  lines,  following  the  fluidity  curves; 
and  maxima  are  found  in  the  acetone-alcohol  curves. 

The  investigation  was  extended  by  McMaster2  in  a  study 
of  lithium  bromide  and  cobalt  chloride.  The  former  behaved 
normally  in  all  the  mixtures  of  the  alcohols  and  water;  that 
is  to  say,  a  minimum  was  noticed  in  the  conductivity  curves 
at  o°  and  25°  in  mixtures  of  the  alcohols  with  water,  while 
the  results  for  mixtures  of  the  two  alcohols  obeyed  the  law 
of  averages  almost  exactly.  In  mixtures  containing  acetone, 
relations  were  found  very  closely  analogous  to  those  obtained 
by  Bingham  in  the  case  of  lithium  nitrate.  The  solutions 
in  alcohol-acetone  gave  maxima  of  conductivity  in  the  75 
per  cent  acetone  mixture;  while  the  solutions  in  water  gave 
minima  at  the  higher  dilutions  and  inflection  points  at  the 
lower  dilutions.  The  unusual  behavior  of  the  acetone  mix- 
tures is  here  again  very  evident. 

Cobalt  chloride,   on  the  other  hand,  gave  unexpected  re- 

1  Am.  Chem.  Journ.,  36,  427  (1906), 
*lbid.,  36,  325  (1906). 


15 

suits.  In  the  first  place,  the  conductivity  of  its  solutions  in 
ethyl  alcohol  is  surprisingly  low,  being  only  about  15  per  cent 
as  great  as  in  water.  In  ethyl  alcohol-water  mixtures,  cobalt 
chloride  gave  an  inflection  point  in  nearly  all  the  solutions, 
but  in  the  curves  for  V  =  200  to  V  =  1600,  at  o°,  the  value 
of  fiv  is  greater  in  the  75  per  cent  than  in  the  50  per  cent  mix- 
ture, thereafter  declining  to  the  lower  values  in  pure  ethyl 
alcohol.  Exactly  the  same  phenomenon  is  shown  by  calcium 
nitrate  in  acetone-water  solutions,  where  the  curves  rise  from 
the  50  per  cent  to  the  75  per  cent  mixture,  and  drop  off  rapidly 
in  pure  acetone.  Rouiller  found  similar  results  for  silver 
nitrate.  In  methyl  alcohol-water  solutions,  cobalt  chloride 
is  normal,  giving  pronounced  minima  in  the  50  or  75  per  cent 
mixtures.  Methyl  alcohol-ethyl  alcohol  solutions  gave  nearly 
straight  lines,  as  did  also  solutions  in  acetone-methyl  alcohol. 
In  the  last  cases  the  fluidity  curves  are  also  nearly  straight 
lines,  but  the  ace  tone- methyl  alcohol  conductivity  curves 
have  a  slope  which  is  the  reverse  of  the  fluidity  curve.  Acetone 
and  ethyl  alcohol  gave  a  maximum  in  the  25  per  cent  mixture. 

In  most  of  the  above  cases,  we  see  that  the  conductivity 
varies  directly  as  the  fluidity,  and  fluidity  minima  are  usually 
accompanied  by  conductivity  minima.  The  converse,  that 
conductivity  minima  were  accompanied  by  fluidity  minima, 
was  not  always  found  to  be  true,  as,  for  instance,  with  cobalt 
chloride  in  acetone-ethyl  alcohol.  Here  a  maximum  of  con- 
ductivity is  found  in  mixtures  giving  a  fluidity  curve  which 
differs  by  less  than  experimental  error  from  a  straight  line. 
Again,  the  conductivity  curves  for  acetone-water  show  in- 
flection points,  while  the  fluidity  curve  has  a  minimum.  These 
apparently  irregular  results  are  to  be  considered  again  in 
the  work  of  Jones  and  Mahin. 

In  explanation  of  the  minimum  of  conductivity,  Jones 
and  McMaster  adopt  the  view  that  the  diminution  in  the 
fluidity  of  the  solvent  is  an  important  factor  in  determining 
the  conductivity  minimum.  But  this  does  not  account  en- 
tirely for  the  phenomenon.  The  change  in  the  size  of  the 
ionic  sphere,  the  atmosphere  surrounding  the  ion,  must  also 
be  considered.  The  velocity  of  the  ion  depends  not  only 


i6 

on  its  composition,  but  also  on  its  attraction  for  the  solvent. 

There  yet  remain  for  consideration  the  several  maxima  of 
conductivity  noticed  in  this  work  as  well  as  in  that  of  Bing- 
ham.  The  discussion  of  the  latter  work  has  shown  that  it 
is  improbable  that  the  maxima  are  due  to  an  increase  in  disso- 
ciating power  in  the  mixture  where  they  occur.  Moreover, 
an  examination  of  the  conductivities  of  lithium  bromide  and 
cobalt  chloride  shows  that  complete  dissociation  is  more  nearly 
reached  in  the  pure  solvents  than  in  the  mixtures  where  the 
maxima  are  found.  Hence,  it  was  concluded  that  the  cause 
of  the  effect  is  primarily  a  change  in  the  dimensions  of  the 
ionic  spheres. 

Some  points  of  interest  were  noted  in  connection  with  the 
temperature  coefficients  of  conductivity  and  of  fluidity.  First, 
in  nearly  every  case  the  temperature  coefficients  of  conduc- 
tivity are  greater  in  the  more  dilute  than  in  the  more  con- 
centrated solutions.  The  work  of  Jones  has  shown  that  in 
practically  all  solutions  there  is  some  combination  between 
solvent  and  solute,  and  that  the  solvates  become  more  com- 
plex as  the  dilution  increases.  Therefore,  change  in  tem- 
perature, which  affects  the  complex  solvates  most,  has  a  greater 
effect  on  the  conductivity  of  the  more  dilute  solutions. 

A  second  point  worth  noting  was  that  in  certain  solutions 
negative  temperature  coefficients  of  conductivity  were  found. 
These  manifested  themselves  in  solutions  of  cobalt  chloride 
in  acetone,  in  75  per  cent  acetone  and  methyl  alcohol,  and 
in  50  and  75  per  cent  acetone  and  ethyl  alcohol.  In  the  75 
per  cent  acetone  and  methyl  alcohol,  when  V  =  200,  the  tem- 
perature coefficient  is  zero. 

The  change  in  conductivity  with  temperature  is  the  alge- 
braic sum  of  two  opposing  influences.  First,  rise  in  tem- 
perature diminishes  dissociation;  secondly,  rise  in  temperature 
is  accompanied  by  an  increase  in  fluidity.  The  first  of  the 
processes  tends  to  decrease  conductivity,  the  second  to  in- 
crease it.  When  the  sum  is  positive,  we  have  increasing 
conductivity  with  rise  in  temperature,  as  is  usually  found  to 
be  the  case.  In  the  one  instance  mentioned  above,  the  two 


I? 

forces  are  equal,  and  the  conductivity  is  independent  of  the 
temperature. 

The  investigation  of  Jones  and  Veazey1  included  a  study 
of  the  behavior  of  copper  chloride  and  potassium  sulphocy- 
anate.  Both  of  these  electrolytes  gave  results  which  were 
almost  entirely  "normal;"  that  is,  conductivity  curves  followed 
fluidity  curves  in  every  case  except  two.  These  exceptions 
were  the  curves  for  copper  chloride  in  mixtures  of  the  alcohols 
with  water.  No  minima  were  found  here  corresponding 
to  the  well-marked  minimum  in  fluidity,  although  the  con- 
ductivities were  always  less  than  required  by  the  law  of  aver- 
ages. An  inflection  point  occurs  between  the  50  and  75  per 
cent  mixtures.  The  conductivity  curves  of  potassium  sulpho- 
cyanate  show  no  such  irregularity,  but  are  in  every  respect 
parallel  to  the  fluidity  curves  of  the  solvents. 

In  addition  to  determining  the  fluidities  of  the  various 
solvent  mixtures,  Jones  and  Veazey  measured  the  fluidities 
of  solutions  of  potassium  sulphocyanate  in  these  mixtures. 
It  was  found  that  in  many  cases  the  fluidity  of  the  solution 
is  greater  than  the  fluidity  of  the  solvent;  in  other  words, 
potassium  sulphocyanate,  under  certain  conditions,  has  a 
negative  viscosity  coefficient.  In  mixtures  of  methyl  alcohol 
and  water,  the  viscosity  of  the  tenth-normal  solutions  is  less 
than  that  of  the  o,  25,  and  50  per  cent  solvent  mixtures,  and 
greater  than  the  75  per  cent  mixture,  becoming  equal  at 
some  point  corresponding  to  about  65  per  cent  alcohol.  The 
same  phenomena  repeat  themselves  in  ethyl  alcohol-water 
mixtures.  With  acetone  and  water,  the  negative  viscosity 
coefficient  again  becomes  apparent,  this  time  only  in  the  o 
and  25  per  cent  mixtures.  In  the  other  mixed  solvents, 
the  viscosity  is  increased  by  the  addition  of  the  solute. 

An  examination  of  the  literature  relating  to  viscosity  brought 
to  light  the  important  fact  that,  in  general,  only  salts  of  potas- 
sium, rubidium,  and  caesium  are  known  to  lower  the  viscosity 
of  water.  Very  few  other  cases  of  negative  viscosity  have 
been  found,  and  not  all  salts  of  these  metals  behave  alike  in 
this  respect.  For  instance,  the  sulphate,  ferrocyanide,  ferri- 

1  Am.  Chem.  Journ.,  37,  405  (1907);  Z.  physik.  Chem.,  61,  641  (1908). 


18 

cyanide,  and  chromate  of  potassium  give  positive  viscosity 
coefficients.  And  it  is  not  remarkable  that  in  the  presence 
of  certain  anions,  the  alkali  cations  do  not  give  negative  vis- 
cosity coefficients.  Viscosity  must  be  considered  to  be  a 
property  which  is  a  function  of  the  nature  of  all  the  particles 
in  a  solution,  and  it  is  perfectly  clear  that  here,  as  in  conduc- 
tivity, two  opposing  influences  may  be  operative,  the  potas- 
sium cation,  for  instance,  tending  to  lower  the  viscosity  and 
the  anion  tending  to  increase  it.  If  the  algebraic  sum  is  posi- 
tive, a  positive  viscosity  results,  and  vice  vena,  the  actual 
viscosity  of  the  solution  being  dependent  on  the  relative  action 
of  the  two  ions. 

The  facts  have  been  presented  showing  that  in  aqueous 
solution,  or  in  solutions  containing  as  much  as  50  per  cent 
of  water,  potassium  sulphocyanate  produces  a  lowering  of 
the  viscosity.  What  is  the  mechanism  of  this  effect? 

The  work  of  Thorpe  and  Rodger  has  shown  that  viscosity 
phenomena  are,  in  all  probability,  dependent  upon  the  fric- 
tional  surfaces  of  the  various  particles  in  any  solution.  If 
the  total  frictional  surface  can  be  diminished  by  any  means, 
other  factors  remaining  constant,  the  viscosity  will  be  lowered. 
We  may  actually  realize  this  by  bringing  into  a  solvent  a  sub- 
stance which  has  a  large  molecular  volume,  or  which  gives 
ions  having  large  ionic  volumes.  The  total  frictional  surface 
proportional  to  the  mass  is  thus  lessened,  since  the  surface 
increases  as  the  square  of  the  diameter  of  the  particles,  while 
the  mass  increases  as  the  cube.  Potassium,  rubidium,  and 
caesium  salts,  as  we  have  said,  lower  the  viscosity  of  water. 
Are  their  atomic  volumes,  accordingly,  larger  than  those  of 
other  elements?  The  periodic  curve  of  atomic  volumes  an- 
swers this  question  at  once.  The  alkali  metals  occupy  the 
maxima  of  the  curve,  and  no  other  metals  have  atomic  volumes 
to  be  compared  with  them.  Moreover,  that  element  having 
the  greatest  atomic  volume — caesium — should  have  the  greatest 
negative  viscosity  coefficient.  This  point  is  soon  tested  by 
reference  to  the  work  of  Wagner.1  If  the  viscosity  of  water 
is  taken  as  unity,  a  normal  solution  of  caesium  chloride  lowers 

1  Z.  physik.  Chem.,  5,  35  (1890). 


19 

it  to  0.9775,  a  normal  solution  of  rubidium  chloride  gives 
0.9846,  and  potassium  chloride  0.9872.  Thus  the  effect  on 
viscosity  varies  directly  as  the  atomic  volume  of  the  cation, 
caesium  having  an  atomic  volume  of  74,  rubidium  of  57,  and 
potassium  47. 

It  will  be  remembered  that  minima  of  fluidity  were  found 
in  mixtures  of  water  with  the  alcohols  or  with  acetone,  accom- 
panied usually  by  minima  in  conductivity.  The  fact  also 
came  out  that  in  those  mixtures  which  have  the  minimum 
fluidity,  the  temperature  coefficients  of  conductivity  are 
largest.  The  explanation  of  this  is  sufficiently  evident.  Each 
solvent,  highly  associated  in  the  pure  condition,  breaks  down 
the  association  of  the  other,  as  shown  by  Jones  and  Murray, 
so  that  the  resulting  mixture  is  composed  of  a  greater  number 
of  smaller  molecules  in  a  given  volume.  Simple  molecules 
would  probably  have  greater  chemical  activity  than  the  more 
complex  ones  and  would  combine  with  the  solute  to  a  greater 
extent.  The  effect  of  heat  on  such  solvates  would  be  greater 
with  increasing  complexity  of  the  solvate.  In  connection 
with  this  breaking  down  of  the  solvents  into  simpler  aggre- 
gates, the  total  internal  frictional  surface  would  be  increased, 
and  an  increase  in  viscosity  is  the  result.  Again,  in  terms  of 
Dutoit  and  Aston's  hypothesis,  the  dissociating  power  of  such 
a  mixture  should  be  less  than  that  of  the  pure  solvents,  and 
this  is  an  important  factor  in  determining  the  conductivity 
minimum,  as  pointed  out  by  Jones  and  Bingham.  It  is  noticed 
that  in  these  mixtures  of  minimum  fluidity,  there  is  a  smaller 
increase  of  conductivity  with  dilution  than  in  the  other  mix- 
tures, and  this  is,  of  course,  a  consequence  of  the  view  here 
adopted. 

In  a  second  communication,1  Jones  and  Veazey  took  up  a 
study  of  solutions  of  tetraethylammonium  iodide — Walden's 
"Normalelektrolyt" — in  mixtures  of  water,  the  alcohols, 
and  nitrobenzene.  The  latter  is  a  solvent  of  a  type  entirely 
different  from  the  hydroxy  compounds  or  acetone,  and  it 
was  important  to  know  whether  the  relations  previously 
found  would  hold  for  mixtures  containing  this  substance. 

1  Z.  physik.  Chem.,  62,  41  (1908). 


20 

In  mixtures  of  both  the  alcohols  with  water,  tetraethyl- 
ammonium  iodide  shows  a  well-defined  conductivity  minimum 
in  the  neighborhood  of  the  50  or  75  per  cent  mixtures  at  both 
o°  and  25°.  In  mixtures  of  the  alcohols  with  each  other, 
no  minima  appeared,  although  the  values  are  less  than  the 
averages.  Mixtures  of  methyl  alcohol  and  nitrobenzene 
behaved  similarly,  but  mixtures  of  ethyl  alcohol  and  nitro- 
benzene gave  a  maximum  in  the  solutions  containing  25  per 
cent  of  the  latter.  The  fluidity  curves  of  mixtures  of  water 
and  the  alcohols  have  already  been  sufficiently  treated,  and 
here,  as  before,  the  conductivity  curves  follow  them  closely. 
The  same  general  relations  appear  in  mixtures  of  nitrobenzene 
and  the  alcohols.  A  fluidity  maximum  shows  itself  in  mix- 
tures containing  25  per  cent  of  nitrobenzene,  with  either 
alcohol,  and  at  o°  and  25°.  Hence,  the  conductivity  curves, 
in  the  case  of  nitrobenzene-ethyl  alcohol  mixtures  at  least, 
follow  the  fluidity  curves,  and  the  variation  with  nitrobenzene- 
methyl  alcohol  is  slight. 

It  has  now  been  shown  that  for  all  the  solvents  worked  with, 
it  is  practically  a  constant  phenomenon  for  conductivity 
curves  to  have  the  same  general  characteristics  as  fluidity 
curves.  On  the  other  hand,  we  must  not  lose  sight  of  the 
fact  that  several  well-marked  exceptions  have  been  found, 
and  notably  in  mixtures  containing  acetone.  Here  the  fluidity 
curves  for  water-acetone  have  minima,  and  for  acetone-alcohol 
are  nearly  straight  lines,  while  the  conductivity  curves  for 
lithium  bromide,  lithium  nitrate,  cobalt  chloride,  and  calcium 
nitrate  show  pronounced  maxima,  or  pseudomaxima.  More- 
over, the  values  of  the  molecular  conductivities  in  acetone 
are  abnormally  low,  except  for  lithium  salts. 

In  the  work  of  Walden,1  already  referred  to,  it  was  found 
that  the  product  of  the  limiting  molecular  conductivity  of 
tetraethylammonium  iodide  and  the  viscosity  of  its  infinitely 
dilute  solutions  is  nearly  a  constant  for  about  thirty  organic 
solvents,  and  equal  to  about  0.7.  Water  and  glycol  are  ex- 
ceptions, giving  products  equal  to  i.o  and  1.32,  respectively. 
The  product  p^  rj  is  also  independent  of  temperature.  There- 

i  Z.  physik.  Chem.,  55,  207  (1906). 


21 

fore,  generally  speaking,  conductivity  varies  as  the  fluidity 
of  the  solvent.  But,  as  we  have  shown,  in  certain  solutions 
containing  acetone,  this  relation  no  longer  holds. 

It  may  further  be  noted  that  Jones  has  shown1  that  cadmium 
iodide  and  ammonium  sulphocyanate,  in  acetone  solutions, 
have  abnormally  high  molecular  weights,  although  such  solu- 
tions conduct  the  current.  He  pointed  out  that  these  facts 
indicate  simultaneous  association  and  dissociation  of  the 
solute;  a  high  concentration  of  molecular  complexes,  which 
causes  an  abnormal  apparent  molecular  weight,  coexisting 
with  a  low  ionic  concentration,  which  causes  a  low  conduc- 
tivity value.  A  consideration  of  these  points  suggested  to 
Jones  and  Mahin  several  lines  of  inquiry,  which  were  taken 
up  in  the  ninth  communication.2  They  sought  to  answer 
the  following  questions : 

1.  Will  those  salts  that  have,   at  ordinary  concentration, 
abnormally   low   values  for   molecular   conductivity   possess, 
when  completely  dissociated,  values  which  are  inversely  pro- 
portional to  the  coefficient  of  viscosity? 

2.  If  so,  is  the  product  of  molecular  conductivity  and  vis- 
cosity constant  for  mixed  solvents  and  at  different  tempera- 
tures ? 

3.  Is  the  value  of  the  constant  the  same  for  different  electro- 
lytes? 

4.  Are   the   abnormal  conductivities  in   acetone   and   mix- 
tures of  acetone  with  other  solvents  due  to  association  of  the 
salt? 

The  first  salt  studied  was  lithium  nitrate.  Extreme  pre- 
cautions were  taken  to  insure  purity  of  the  solvents,  and  meas- 
urements were  carried  to  dilutions  as  high  as  200,000  liters 
wherever  practicable.  Under  these  conditions,  the  conduc- 
tivity curves  assumed  forms  which  differed  markedly  from 
those  obtained  for  dilutions  between  10  and  1600  liters,  and 
which  closely  resembled  the  fluidity  curves.  Moreover, 
the  product  of  the  viscosity  coefficient  and  the  maximum 
conductivity  in  solutions  of  acetone  mixed  with  the  alcohols 

1  Am.  Chem.  Journ.,  27,  16  (1902). 

2  To  appear  in  Z.  physik.  Chem.,  August,  1909. 


22 

has  a  mean  value  of  0.62,  agreeing  well  with  Walden's  value 
of  0.70  for  simple  *  solvents,  and  being  independent  of  tem- 
perature. With  acetone-water  mixtures,  the  product  varies 
between  i.oo,  the  value  for  water,  and  0.63,  the  value  for 
acetone. 

Some  determinations  of  the  molecular  weight  of  lithium 
nitrate  in  acetone  by  the  boiling  point  method  brought  out 
interesting  results.  The  concentration  of  the  solutions  varied 
roughly  between  normal  and  tenth-normal.  Kven  in  the  more 
dilute  solutions,  the  indicated  molecular  weight  was  83.1, 
while  the  value  required  by  the  formula  LiNO3  is  69.07.  This 
accounts  for  the  low  conductivity  of  lithium  nitrate  in  acetone 
solutions  of  not  very  great  dilution. 

As  already  stated,  cadmium  iodide  was  found  by  Jones  to 
be  associated  in  acetone,  and  a  study  of  this  salt  was  next 
made.  Results  in  this  case  were  not  so  satisfactory  as  with 
lithium  nitrate.  The  conductivity  curves  show  signs  of  re- 
gaining a  similarity  to  the  fluidity  curves,  but  the  resemblance 
is  not  so  close  as  with  the  other  salt.  Moreover,  the  product 
of  the  viscosity  by  the  maximum  conductivity  is  irregular. 
The  conductivity  data  show  that  in  most  cases  a  limiting 
value  was  not  reached  with  cadmium  iodide,  and  some  solu- 
tions more  nearly  approached  the  true  values  than  others, 
thus  causing  the  fluctuations  in  the  value  of  the  product. 
It  must  be  borne  in  mind  that  conductivity  measurements 
at  dilutions  so  great  (400,000  liters)  that  the  correction  for 
the  conductivity  of  the  solvent  often  amounts  to  more  than 
50  per  cent  of  the  total,  are  being  made  at  a  point  where  the 
method  is  taxed  rather  beyond  its  limitations;  and  it  is  not 
surprising  that  even  with  the  utmost  precautions,  concordant 
results  are  not  obtained.  The  failure  of  cadmium  iodide 
to  follow  the  behavior  of  lithium  nitrate  in  very  dilute  solu- 
tions is  merely  negative  evidence,  and  must  be  weighed 
as  such. 

Some  boiling  point  determinations  of  cadmium  iodide  in 
acetone  were  made,  and  here  too,  considerable  polymeriza- 
tion was  found.  In  a  0.09  normal  solution,  the  indicated 
molecular  weight  was  448,  calculated  364. 


23 

Thus,  the  apparent  exceptions  to  the  relations  found  by 
Jones  and  his  coworkers  are  seen  to  vanish  when  we  are  deal- 
ing with  what  are  practically  infinitely  dilute  solutions.  The 
investigations  have  dealt  with  twelve  electrolytes  and  six 
solvents,  and  in  every  instance  the  same  relations  are  found 
to  hold,  connecting  the  molecular  conductivity  with  the 
fluidity. 

Jones  and  Mahin1  also  made  a  study  of  the  conductivity 
and  viscosity  of  lithium  nitrate  in  ternary  mixtures  of  the 
four  solvents  used  above.  The  results  were  about  what  would 
be  expected  from  a  knowledge  of  the  solutions  in  binary  mix- 
tures. The  conductivity  curves,  in  the  great  majority  of 
cases,  followed  the  fluidity  curves,  and  no  new  relations  were 
brought  to  light. 

As  a  result  of  this  work,  we  may  make  the  general  state- 
ment: If  we  mix  methyl  and  ethyl  alcohols,  or  methyl  alco- 
hol and  acetone,  the  conductivity  curves  are  very  close  to 
straight  lines,  and  the  fluidities  of  the  mixture  are  nearly 
additive.  Take,  for  instance,  the  last  case  mentioned.  The 
table  shows  the  fluidities  of  various  mixtures  of  methyl  alcohol 
with  acetone  at  o°,  as  determined  by  the  viscometer,  and  also 
as  calculated  from  those  of  the  two  components. 

Fluidity    of  Mixtures  of    Methyl  Alcohol  and  Acetone,  at  o°. 

Per  cent  acetone  o  25  50  75         100 

Fluidity  observed  122.2     153.9     187.4     222.2     244.1 

Fluidity  calc.  ...        152.7     183.2     213.7 

The  observed  fluidities  are  very  nearly  the  averages  corre- 
sponding to  the  different  mixtures.  On  the  other  hand,  if 
we  mix  water  with  the  alcohols,  or  with  acetone,  there  is  inter- 
action between  the  components  of  the  mixture,  and  certain 
of  its  physical  properties  are  found  no  longer  to  bear  simple 
relations  to  the  properties  of  the  single  solvents.  Otherwise 
expressed,  the  law  of  averages  is  not  followed,  and  the  proper- 
ties of  the  mixture  are  not  additive.  Hence,  we  may  con- 
clude that  water,  mixed  with  the  other  three  solvents,  causes 
some  deep-seated  change  in  the  state  of  molecular  aggrega- 

1  Am.  Chem.  Journ.,  41,  433  (1909). 


24 

tion  of  the  liquid  molecules,  while  mixing  the  three  organic 
solvents  with  each  other  causes  no  such  change.  The  various 
mixed  solvents  may  therefore  be  divided  into  two  classes, 
those  not  containing  water,,  with  properties  nearly  or  quite 
additive,  and  those  containing  water,  with  properties  that 
are  not  the  averages  of  the  two  components. 

PART  II. 

It  is  thus  seen  that  certain  definite  relations  exist  between 
the  conductivity  of  various  electrolytes  dissolved  in  binary 
mixtures  of  four  solvents,  and  the  viscosity  of  their  solutions. 
It  was  of  interest  to  know  whether  similar  relations  would 
hold  when  one  of  the  component  solvents  had  a  viscosity 
much  greater  than  that  of  the  other;  in  other  words,  whether 
the  effect  of  one  solvent  on  another  follows  the  same  laws, 
no  matter  what  substances  are  used.  The  solvent  eminently 
suited  for  this  purpose  is  glycerol.  Not  only  is  its  viscosity 
enormously  greater  than  that  of  any  other  homogeneous 
liquid  at  ordinary  temperatures,  but  several  of  its  physical 
constants  would  lead  us  to  expect  glycerol  to  be  well  adapted 
as  a  solvent  in  making  conductivity  measurements.  The 
dielectric  constants  and  association  factors  of  the  solvents 
used  in  the  previous  work  are  given  in  Table  I.  The  dielec- 
tric constants  are  taken  from  the  work  of  Drude1  and  were 
all  determined  in  the  neighborhood  of  18°,  and  the  associa- 
tion factors  are  taken  from  the  work  of  Ramsay  and  Shields,2 
and  refer  to  nearly  the  same  temperature. 

Table  L 

Solvent.  Dielectric  constant.        Association  factor. 

Water  81.7  4.00 

Methyl  alcohol  32.5  3-43 

Ethyl  alcohol  21.7  2 . 74 

Acetone  20.7  1.26 

Glycerol  has  a  dielectric  constant  of  16.5  at  18°,  and  hence, 
in  terms  of  the  Thomson-Nernst  rule,  should  have  a  fairly 
high  dissociating  power.  Moreover,  if  we  assume  Dutoit 

1  Wied.  Ann.,  60,  500. 

2  Z.  physik.  Chem.,  12,  433  (1893). 


25 

and  Aston's  hypothesis  to  hold  even  approximately  for  glycerol, 
the  association  factor  of  the  latter,  1.80  at  20°,  would  lead 
to  the  same  conclusion.  The  conductivity  data  will  show 
that  these  expectations  are  well  founded,  and  that  glycerol  is, 
in  all  probability,  a  solvent  with  a  dissociating  power  rather 
above  the  average. 

Glycerol  as  a  Solvent. 

It  has,  of  course,  been  known  for  a  long  time  that  glycerol 
has  remarkable  solvent  properties.  Not  only  will  it  dissolve 
all  deliquescent  salts,  such  as  many  compounds  of  lithium 
and  calcium,  but  it  also  takes  up  large  quantities  of  nearly 
all  the  halogen  salts  of  the  common  metals,  including  even 
those  which  are  difficultly  soluble  in  water,  as  well  as  many 
sulphates,  nitrates,  etc.  In  addition,  the  alcohol  groups  of 
glycerol  react  with  metallic  oxides  and  hydroxides,  forming 
glycerates  by  a  process  analogous  to  the  solution  of  sodium 
or  potassium  hydroxides  in  alcohol. 

In  spite  of  the  ease  with  which  very  pure  glycerol  can  be 
obtained  in  large  quantity,  very  little  work  has  been  done 
with  solutions  in  it.  In  various  branches  of  manufacture, 
and  especially  in  pharmacy,  it  has  long  had  extensive  use  as 
a  solvent,  but  no  systematic  study  has  been  made  of  the  prop- 
erties of  its  solutions. 

Cattaneo1  measured  the  conductivity  of  a  number  of  halogen 
salts  of  the  metals  in  glycerol,  and  found  that  the  conduc- 
tivities are  smaller  than  the  corresponding  values  in  water 
or  alcohol,  but  greater  than  those  in  ether.  He  also  states 
that  the  molecular  conductivity  increases  only  in  the  case 
of  chlorides.  This  last  statement  is  not  at  all  confirmed  by 
the  present  work. 

Schottner2  carried  out  an  extensive  investigation  on  the 
viscosity  of  glycerol  and  of  some  of  its  mixtures  with  water. 
Arrhenius3  measured  the  viscosity  of  certain  organic  sub- 
stances, including  glycerol,  in  aqueous  solution,  and  found 
that  the  decrease  of  y  with  rising  temperature  is  greatest 

1  Rend.  Accad.  Line.  [5],  2,  II,  112  (1893). 

2  Wien.  Ber.,  77,  2,  682  (1878). 

3  Z.  physik.  Chem.,  1,  289  (1887). 


26 

when  TJ  is  large.  Schall  and  van  Rijn1  determined  the 
relative  times  of  flow  of  various  mixtures  of  glycerol  with 
small  quantities  of  water  and  alcohol. 

EXPERIMENTAL. 

Condiictimty  Apparatus. 

The  conductivity  measurements  were  made  by  the  Kohl- 
rausch  method,  using  a  wire  bridge  and  telephone  receiver. 
The  bridge  wire  was  calibrated  and  found  to  be  of  uniform 
resistance  throughout.  The  conductivity  cells  were  of  the 
form  used  by  Jones  and  Bingham  and  subsequent  workers 
in  this  laboratory.  For  use  with  the  solutions  in  pure  glycerol, 
two  (jells  of  a  different  type  were  used.  The  electrodes  in 
one  cell  consisted  of  two  concentric  platinum  cylinders,  about 
7  cm.  long,  and  18  and  22  mm.  in  diameter.  They  were  main- 
tained at  a  constant  distance  apart  of  about  2  mm.  by  means 
of  several  drops  of  fusion  glass  attached  to  the  edges  of  the 
cylinders.  The  constant  was  very  low,  about  4.30.  The 
other  cell  had  as  electrodes  three  cylinders,  the  outer  and 
inner  being  joined  by  a  thick  branching  platinum  wire,  and 
forming  one  electrode,  while  the  middle  cylinder  formed  the 
other.  Drops  of  fusion  glass  also  served  here  to  keep  the 
electrodes  at  a  constant  distance  apart  of  about  1.5  mm. 
The  cell  constant  was  about  2.35.  The  electrodes  of  both 
cells  were  used  without  being  covered  with  platinum  black, 
and  it  was  possible  to  obtain  very  sharp  minima  on  the  bridge 
with  them.  For  instance,  when  the  cell  contained  conduc- 
tivity water,  and  a  resistance  of  one  or  two  thousand  ohms 
was  introduced  into  the  circuit,  the  bridge  could  easily  be 
read  at  points  two  mm.  on  each  side  of  the  true  minimum. 
This  form  of  cell  has  proved  itself  to  be  especially  adapted 
to  work  with  very  viscous  solutions.  The  large  electrode 
surface  permits  of  the  cylinders  being  several  mm.  apart, 
without  making  the  "capacity"  of  the  cell  too  great;  and 
this  feature  alone  is  of  great  advantage,  as  it  allows  very 
thick  liquids  to  fill  all  the  space  between  the  electrodes,  without 
the  danger  of  imprisoning  air  bubbles.  The  escape  of  the 

1  Z.  physik.  Chem.,  23,  329  (1897). 


27 

latter  is  further  facilitated  by  the  vertical  position  of  the 
cell  walls.  The  "constants"  of  both  cells  showed  only  ex- 
tremely slight  variation  throughout  the  work. 

The  conductivity  measurements  are  expressed  in  reciprocal 
Siemens' s  units,  and  the  cell  constants  were  determined  by 
means  of  a  fiftieth-normal  potassium  chloride  solution,  the 
molecular  conductivity  of  which  was  taken  as  129.7  at  25°. 

Measurements  were  made  at  25°  and  35°.  Glycerol,  when 
maintained  at  o°  for  a  long  period,  undergoes  a  gradual  change, 
resulting  sometimes  in  the  deposition  of  crystals.  On  this 
account,  and  for  the  reason  that  at  low  temperatures  the 
substance  is  so  extremely  immobile  that  viscosity  determina- 
tions are  almost  impossible,  no  measurements  were  made 
at  o°,  as  has  been  the  custom  in  these  investigations.  The 
temperature  coefficients  of  conductivity  and  viscosity  are 
therefore  not  strictly  comparable  with  those  obtained  by 
other  workers  for  the  same  solutions  between  o°  and  25°. 

The  constant- temperature  baths  were  of  the  form  described 
before,  and  were  maintained  constant  within  o°.O3  of  the 
desired  temperatures.  The  thermometers  were  compared 
with  a  certificated  Reichsanstalt  instrument.  The  measuring 
flasks  were  calibrated  to  hold  aliquot  parts  of  the  true  liter 
at  20°,  and  solutions  were  brought  to  within  o°.2  of  this  tem- 
perature before  filling  to  the  mark. 

Solvents. 

Glycerol. — The  glycerol  used  was  Kahlbaum's  "Glycerin, 
1.26."  Two  determinations  of  different  lots  gave  the  same 
density,  Dli  =  1.2586.  The  specific  conductivity  varied  from 
0.5  X  io~7  to  0.7  X  io~7  at  25°.  Some  of  the  glycerol  was 
distilled  under  diminished  pressure,  boiling  at  160°  under 
a  pressure  of  6  mm.  The  specific  conductivity  was  not  changed 
by  this  process,  and  the  remainder  of  the  glycerol  was  used 
without  further  treatment. 

Water. — The  water  was  purified  essentially  by  the  method 
of  Jones  and  Mackay,1  with  a  slight  modification.  The  prac- 
tice heretofore  has  been  to  distil  ordinary  distilled  water 

1  Am.  Chem.  Journ.,  17,  83  (1895). 


28 

from  acidified  potassium  dichromate  to  destroy  organic  matter 
and  retain  ammonia,  and  then  to  redistil  from  a  weaker 
chromic  acid  solution,  forcing  the  steam  from  the  second 
distillation  through  a  solution  of  barium  hydroxide.  There 
can  be  no  doubt  that  water  prepared  in  this  way  still  con- 
tains large  quantities  of  carbon  dioxide.  The  extreme  rapidity 
with  which  the  current  of  steam  passes  through  the  alkaline 
solution  makes  it  impossible  for  the  latter  to  come  in  contact 
with  all  of  the  vapor,  and  some  .of  the  carbon  dioxide  escapes 
with  the  steam  to  be  condensed,  giving  water  with  a  con- 
ductivity which  has  generally  been  about  2  X  icf"6  at  25°. 
If,  however,  the  second  distillation  is  made  from  a  solution 
containing  barium  hydroxide  instead  of  acidified  dichromate, 
the  conductivity  of  the  water  is  lowered  considerably.  Nearly 
all  of  the  carbon  dioxide  is  retained,  and  the  conductivity 
of  the  water  thus  purified  has  rarely  risen  over  1.5  X  lo""6, 
and  was  many  times  as  low  as  1.2.  In  addition,  the  alkaline 
solution,  probably  owing  to  the  presence  of  the  fine  crystals 
of  barium  carbonate,  boils  more  quietly  than  the  acid  solu- 
tion, with  entire  absence  of  bumping,  and  with  consumption 
of  much  less  gas. 

Ethyl  and  Methyl  Alcohols. — These  were  purified  by  boil- 
ing the  commercial  articles  with  fresh  lime  for  a  day,  and 
then  distilling  again  from  more  lime  without  transferring 
the  alcohol  in  the  air.  A  third  distillation  from  lime  was 
made  if  the  specific  gravity  of  the  second  distillate  showed 
the  presence  of  any  appreciable  quantity  of  water.  Several 
more  distillations  were  then  made  through  a  block- tin  con- 
denser. The  conductivity  of  the  ethyl  alcohol  ranged  between 
1.2  X  io~7  and  1.8  X  io~7,  although  in  one  case  it  was  as 
low  as  0.9  X  io~7.  The  value  for  the  methyl  alcohol  was 
about  1.5  X  io~6  at  25°. 

Work  with  mixtures  containing  acetone,  which  it  was  hoped 
would  yield  some  interesting  results,  had  to  be  given  up, 
since  glycerol  and  acetone  are  only  slightly  miscible. 

The  mixed  solvents  are  made  up  on  a  volume  basis,  and 
in  every  case  throughout  the  work,  unless  otherwise  speci- 


29 

fied,  "n  per  cent  A  and  B"  means  n  cc.  of  solvent  A  diluted 
to  100  cc.  with  solvent  B. 

Solutions. 

All  solutions  were  made  on  a  volume- normal  basis,  at  20°, 
by  direct  weighing  of  the  anhydrous  salts.  A  tenth-normal 
mother  solution  was  first  made,  from  which  the  fiftieth  and 
hundredth-normal  solutions  were  prepared  by  dilution.  The 
hundredth-normal  solution  then  served  as  a  mother  solution 
for  the  two-,  four-,  and  eight-hundredth-normal  solutions, 
and  from  the  last  named  the  sixteen-hundredth-normal  was 
prepared.  The  dilutions  were  made  by  means  of  calibrated 
flasks  and  burettes.  It  was  found  that  if  a  little  time  was 
given,  the  solutions  containing  25  and  50  per  cent  of  glycerol 
would  drain  as  completely  as  aqueous  solutions,  and  the  same 
calibration  was  used  for  all  three.  With  the  75  per  cent 
solutions,  and  especially  with  those  in  pure  glycerol,  the  drain- 
ing was  incomplete,  even  though  the  burette  stood  two  days. 
Accordingly,  a  different  calibration  was  made  for  each  of  the 
three  mixed  solvents  containing  75  per  cent  of  glycerol,  and 
for  the  pure  glycerol  itself.  The  amount  to  be  delivered  was 
run  at  a  fixed  rate  of  flow  into  a  weighing  glass,  and  its  weight 
divided  by  the  density  of  the  solvent  at  20°.  The  difference 
between  the  volume  thus  found  and  the  volume  read  off 
was  the  amount  clinging  to  the  walls  of  the  burette,  and  this 
quantity,  which  was  about  0.60  cc.  for  25  cc.  of  glycerol, 
was  added  with  each  measurement  of  the  solutions.  It  was 
of  course  necessary  to  run  the  solutions  out  between  the  same 
two  points  on  the  burette  each  time,  as  otherwise  the  mean 
hydrostatic  pressure  would  vary,  causing  corresponding 
variations  in  the  rate  of  flow,  with  a  marked  effect  on  the 
amount  which  did  not  drain  out.  This  precaution  is  im- 
portant, as  shown  by  the  fact  that  a  volume  of  glycerol  drawn 
off  between  o  and  25  on  the  burette  lacked  0.65  cc.  of  25  cc., 
while  the  same  apparent  volume,  taken  between  24  and  49, 
was  0.35  cc.  less  than  the  amount  desired.  The  water  calibra- 
tion showed  that  this  difference  was  not  due  to  a  great  irregu- 
larity in  the  diameter  of  the  burette.  Another  point  which 


30 

must  be  noted  is  the  necessity  of  keeping  the  temperature 
of  the  working  room  very  constant  while  measuring  glycerol. 
The  changes  in  volume  of  the  glycerol  are  inconsiderable 
compared  with  the  great  changes  in  fluidity,  and  a  calibration 
made  for  20°  would,  by  reason  of  the  much  greater  fluidity 
of  glycerol  at  a  higher  temperature,  be  very  inaccurate  at  22°. 

In  view  of  the  fact  that  so  little  work  has  been  done  with 
solutions  in  glycerol,  a  few  details  of  a  practical  nature  may 
not  be  out  of  place.  In  spite  of  the  great  solvent  power  of 
glycerol,  the  actual  rate  of  solution  is  very  slow,  and  most 
substances  can  be  dissolved  only  after  a  great  deal  of  shaking 
and  heating.  It  was  customary  in  this  work  to  heat  the 
glycerol  to  almost  100°  before  adding  it  to  the  salt  in  the 
measuring  flask.  At  this  temperature,  glycerol  is  quite  fluid, 
and  its  solvent  action  is  greatly  enhanced.  Nevertheless, 
it  required,  with  lithium  bromide  and  cobalt  chloride,  nearly 
three  hours  of  practically  continuous  shaking,  with  the  tem- 
perature at  about  8o°— 100°,  to  effect  the  complete  solution 
of  one  or  two  grams  of  the  salts  in  100  cc.  of  glycerol.  Potas- 
sium iodide,  on  the  other  hand,  dissolved  as  soon  as  the  glycerol 
was  warmed  slightly,  and  gave  a  clear  solution  in  less  than 
five  minutes.  In  view  of  the  close  relation  of  glycerol  to  the 
alcohols,  and  of  the  very  slight  solubility  of  potassium  iodide 
in  absolute  alcohol,  this  behavior  is  surprising. 

Much  annoyance  is  caused  by  the  ease  with  which  glycerol 
imprisons  air  bubbles,  which  may  require  hours  to  rise.  Espe- 
cially is  this  likely  to  occur  when  the  substance  is  poured 
into  a  burette.  This  difficulty  may  be  obviated,  however, 
by  pouring  the  solutions  in  while  hot,  in  which  case  the  air 
bubbles  will  rise  fairly  rapidly;  or  by  pouring  the  solutions 
in  such  a  manner  that  the  descending  stream  does  not  strike 
the  walls  of  the  burette  except  at  the  highest  point  to  which 
the  burette  is  to  be  filled.  Thus  manipulated,  the  glycerol 
flows  down  the  burette  walls  without  enclosing  any  air,  and 
moreover,  no  time  is  lost  in  waiting  for  the  upper  part  of  the 
burette  to  drain  before  taking  the  initial  reading. 

Viscosity. 
The  determinations  of  viscosity  were  made  by  means  of 


several  Ostwald  viscometers,1  or  this  form  as  modified  by 
Jones  and  Veazey.2  For  the  solutions  in  pure  glycerol, 
as  well  as  for  the  solutions  containing  75  per  cent  of  glycerol, 
viscometers  of  very  large  bore  were  necessary.  Two  of  these, 
made  for  us  by  Eimer  and  Amend,  were  very  satisfactory. 
The  small  bulb  had  a  capacity  of  about  4  cc.,  and  the  larger 
of  about  30  cc.  The  "  capillaries,"  having  internal  diameters 
of  i.i  and  2  mm.,  respectively,  were  12  cm.  long.  As  the  time 
of  flow  of  water  through  these  viscometers  was  less  than  ten 
seconds,  it  was  of  course  necessary  to  calibrate  them  by  using 
a  more  viscous  liquid,  the  viscosity  of  which  was  known. 
For  this  purpose,  the  viscosities  of  several  solutions,  contain- 
ing about  50  per  cent  of  glycerol,  were  determined  in  the 
smaller  instruments,  and  then  the  times  of  flow  of  these  liquids 
through  the  large  viscometers  were  noted.  A  fixed  amount 
of  solution  was  introduced  into  the  viscometer  from  a  pipette, 
and  after  being  raised  to  the  upper  mark  by  air  pressure,  was 
allowed  to  run  through  the  capillary  by  its  own  weight.  The 
times  of  flow  were  read  with  an  accurate  stopwatch.  The 
viscosities  were  calculated  from  the  formula 

r  st 


where  T?O,  s0,  and  t0  are  the  viscosity,  density,  and  time  of 
flow,  respectively,  of  pure  water,  and  TJ,  s,  and  t  the  correspond- 
ing values  for  the  liquid  in  question.  The  values  of  TJO  at  25° 
and  35°  are  taken  from  Thorpe  and  Rodger's  work2  on  vis- 
cosity, being  0.00891  at  25°  and  0.00720  at  35°.  Fluidity, 

expressed  by  <j>,  is  equal  to  -,  and  the  temperature  coefficients 

"n 
of  fluidity  are  calculated  from  the  formula 

temp.coef.  <fr  =  ~1-. 


.  . 

£25  10 

The  densities  of  the  solutions  were  determined  in  pycnom- 
eters  of  the  form  described  by  Jones  and  Veazey.3 


1  Phys.-chem.  Mess.,  2nd  Ed.,  p.  260. 

2  Phil.  Trans.,  185,  A,  307  (1894). 

3  Z.  physik.  Chem.,  61,  651  (1908). 


32 

The  measurement  of  viscosity,  for  some  reason,  seems 
to  be  beset  with  much  greater  experimental  error  than  would 
be  expected,  considering  the  simple  nature  of  the  operation. 
The  values  given  in  Landolt-Boernstein's  "Tabellen"  often 
show  differences  of  more  than  one  per  cent  in  the  results  of 
various  observers.  During  the  present  work,  it  was  found 
to  be  almost  impossible  to  get  results  that  would  agree  even 
fairly  well  in  duplicate  determinations.  It  may  at  first  sight 
be  supposed  that  by  using  three  "steps"  to  determine  the 
viscosities  of  the  thicker  solutions,  as  was  done  in  this  work, 
experimental  error  is  introduced  at  each  step,  so  that  the 
values  found  by  means  of  instruments  with  wide  capillaries 
would  necessarily  be  of  doubtful  accuracy.  As  a  matter  of 
fact,  though  experimental  error  is  introduced,  the  departure  of 
the  values  found  from  the  true  values  is  influenced  much  less 
by  this  fact  than  by  an  inherent  difficulty  in  the  method. 

trY  *•/)/ 

The  Poisseuille  formula  for  determining  viscosity  is  v  =    0  7    , 

8/77 

where  v  is  the  volume  of  liquid,  whose  viscosity  coefficient 
is  rj,  which,  under  a  pressure  p,  will  flow  in  the  time  t  through 
tube  of  length  /  and  radius  r.  In  deriving  this  formula,  the 
liquid  is  considered  as  leaving  the  tube  with  a  kinetic  energy 
of  zero,  which,  manifestly  is  an  impossible  condition  in  prac- 
tice. If  the  liquid  flows  out  of  the  tube  with  a  positive  kinetic 
energy,  a  correction  must  be  introduced.  On  rearranging 
the  formula,  with  the  correction,  it  becomes 

_  irr*pt         vd 

77  ~  :  ~       '  " 


where  d  is  the  density  of  the  liquid.  In  determining  viscosities 
by  the  relative  method  —  that  is,  by  means  of  the  Ostwald 
viscometer  —  the  corrected  formula  is  rarely  used.  For  two 
liquids  flowing  by  their  own  weight  through  the  same  instru- 
ment, between  the  same  differences  in  level, 


33 
But 


Pi  __  Pi9h  __  Pi 


whence  —  =  —  1,  which  is  the  ordinary  formula. 

>/2  P2*2 

It  is  evident  from  the  corrected  formula  that  when  t  is 
smallest,  the  correction  is  greatest.  Hence,  a  greater  error 
is  introduced  by  measuring  the  viscosity  of  a  liquid  whose 
time  of  flow  is  much  greater  than  that  of  the  standard,  than 
in  the  case  of  one  with  nearly  the  same  viscosity  as  the  stand- 
ard. In  other  words,  the  error  would  be  a  minimum  if  t 
could  be  kept  constant.  Therefore,  the  error  is  kept  lowest 
by  using  in  each  instrument  liquids  whose  times  of  flow  do 
not  differ  too  greatly  from  t0.  As  the  correction  is  always 
negative,  the  viscosity  of  a  liquid  determined  without  using 
intermediate  steps  should  be  greater  than  if  several  viscometers 
are  used.  This  is  illustrated  in  the  case  of  75  per  cent  glycerol 
and  methyl  alcohol  at  25°.  T  is  the  time  of  flow. 

Table  II. 

T.                       T.  T. 

50  per  cent      50  per  cent  75  per  cent 

Viscom-         T.            glycerol  and        glycerol  glycerol  and 

eter.        Water,    methyl  alcohol,  and  water,  methyl  alcohol.             t). 

A    74.4    749.0    450.0    4465-0    0.61735 

1  74.7      45.7      445.6     0.6073 

2  i4J-7    0.6073 

Here  i)  is  calculated  by  the  following  methods: 

For  viscometer  A.  ,  -  aoo89i  X  4465  X  1.1546  _  o  6l?35 

i  X  74-4 

(1.1546  is  the  density  of  75  per  cent  glycerol  and  methyl 
alcohol). 

For  viscometer  i.  The  viscosities  of  50  per  cent  glycerol 
and  water,  and  50  per  cent  glycerol  and  methyl  alcohol,  were 
determined  in  A;  then  from  the  times  of  flow  of  these  solu- 
tions through  i,  two  values  were  obtained  which  were  used 
to  determine  viscosities  in  i,  and  the  mean  value  of  y  for  75 
per  cent  glycerol  and  methyl  alcohol  is  determined  from  them, 
using  T  =  445.6.  The  same  process  is  employed  for  viscometer 


34 

2.  It  is  seen  that  t]  determined  by  direct  comparison  with 
water  is  greater,  as  it  should  be,  than  i)  determined  by  using 
liquids  of  intermediate  viscosities  in  several  instruments. 

Lithium  Bromide. 

The  lithium  bromide  gave  a  flame  test  which  showed  no 
appreciable  impurity.  It  was  dried  to  constant  weight  at 
150°,  and  was  again  dried  after  each  exposure  to  the  air. 
Table  III.  gives  the  molecular  conductivities  of  lithium  bromide 
in  pure  glycerol  at  25°,  35°,  and  45°.  It  will  be  noticed 
that  while  the  values  of  pv  are  very  small,  yet  they  show  a 
regular  increase  with  dilution,  as  is  the  case  with  all  liquids 
having  a  marked  dissociating  power. 


Table  III. — Conductivity   of  Lithium  Bromide  in  Glycerol  at 
25°,  35°,  and  45° • 


Temperature 
coefficients. 

Temperature 
coefficients. 

V. 

Atz/250. 

(0035°. 

Hit/450. 

25°-35°. 

35°-45°. 

10 

0.236 

0.485           < 

).907 

o.  106 

0.0871 

50 

0.26O 

0.540            ] 

.010 

o.  107 

0.0881 

100 

0.270 

0-555         'ft 

.041 

o.  106 

0.0875 

20O 

0.272 

0.565            3 

.050 

o.  106 

0.0868 

400 

0.275 

0.572            1 

.070 

0.108 

0.0871 

8oo 

0.280 

0-579 

•085 

0.107 

0.0874 

1600 

0.287 

0-593            1 

[  .109 

o.  107 

0.0871 

Table  IV. — Conductivity  of  Lithium  Bromide  in  Water  at  25° 

and  35°. 


V. 

10 

50 

100 
2OO 
4OO 
800 
1600 


91.8 
101  .  I 
103.0 
105.2 
107.2 
II4.4 
II4.6 


II0.7 
121  .9 
124.4 
127.4 
I30.I 
I36.I 
137-5 


Temperature 
coefficients. 

0.0205 
0.0206 
0.0208 
O.O2I9 
0.0213 
0.0222 
O.O2OO 


35 

Table  V. — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
25  per  cent  Glycerol  and  Water  at  25°  and  55°. 

Temperature 
V.  /it/25  °.  /*^35°.  coefficients. 

10  45.6  57.4  0.0257 

50  49-6  62.5  0.0261 

100  50.8  64.0  0.0260 

200  52.8  66.7  0.0264 

400  52.2  65.5  0.0255 

800  54.0  69.4  0.0285 

1600  54.9  71.5  0.0300 

Table  VI. — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
50  per  cent  Glycerol  and  Water  at  25°  and  35°. 

Temperature 
V.  /J.v25°.  pv35°.  coefficients. 

10  17.3  23.4  0.0351 

50  18.8  25.4  0.0348 

ioo  19.1  25.7  0.0346 

200  19.5  26.3  0.0350 

400  20.0  27.0  0.0351 

800  21.4  28.9  0.0352 

1600  21.7  29.5  0.0361 

Table  VII. — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
75  per  cent  Glycerol  and  Water  at  25°  and  55°. 

Temperature 
V.  /*z,25°.  /-Cz/350.  coefficients. 

10        3.84        5.96        0.0552 

50  4-23  6.56  0.0552 

ioo        4.27        6.63        0.0551 

200  4.43  6.89  0.0557 

400  4.51  6.99  0.0552 

800  4-4°  6.89  0.0566 

1600  4.47  6.99  0.0567 

Table  VIII. — Conductivity  of  Lithium  Bromide  in  Ethyl  Alcohol 
at  25°  and  35°. 

Temperature 
V.  /*z/25°.  fJ.v35°.  coefficients. 

10        15.8        18.4       0.0162 

50       23.0        26.7       0.0161 

ioo       25.9       30.3        0.0169 

200  29.2  33.6  0.0150 

400  3I.I  36.5  O.OI7I 

800  33.3  39.2  0.0179 

1600  35-1  41.6  O.OI86 


36 

Table  IX.  —  Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
25  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 


V. 

Hv25°. 

/tiz/350. 

coefficient 

10 

50 

7-26 

9-49 

9-32 
12.23 

0.0283 
0.0289 

00 

10.00 

12.94 

0.0294 

00 

10.93 

14.  II 

0.0291 

.00 
00 
00 

II.  21 

11.68 

12.02 

I4-5I 
I5.I6 

I5-72 

O.O294 
0.0298 

o  .  0308 

Table  X.  —  Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
50  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  55°. 

Temperature 
V.  Hv25°.  /tz/35°.  coeffi<^ents. 


10 

2.91 

4-25 

0.0462 

50 

3-40 

4-97 

0.0459 

IOO 

3.6l 

5-29 

o  .  0466 

2OO 

3-85 

5-6i 

0.0458 

400 

3-85 

5-64 

o  .  0466 

800 

3.98 

5-86 

0.0474 

1600 

4-02 

5-89 

o  .  0466 

Table  XL — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
75  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  fJLz/25°.  fJ.v35°.  coefficients. 

10       0.947       1.62        0.0710 

50  I. 08  1.85  0.07II 

loo        1.14        1.95        0.0719 

200  I.I4  1.95  0.0718 

400  I.I9  2.06  0.0720 

800  I.l8  2.02  0.0713 

1600  1.25  2.15  0.0724 

Table  XI L — Conductivity  of  Lithium  Bromide  in  Methyl  Alcohol 
at  25°  and  35' 


Temperature 

V. 

/*z/25°. 

/AiX55°. 

coefficients. 

10 

50.0 

56.4 

0.0127 

50 

64.3 

72-9 

0.0134 

IOO 

69.4 

78.4 

0.0129 

200 

74-i 

84.0 

0.0134 

400 

77-4 

87-4 

0.0129 

800 

79-9 

89.7 

O.OI24 

1600 

81.9 

93-1 

0.0137 

37 

Table  XIII. — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
25  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  /*z/25°.  /iz£5°.  coefficients. 

10       21.3       25.8       0.0214 

50  25.5  30.9  0.0210 

loo       27.1        32.9       0.0213 

2OO  28  9  35.3  0.0222 

400  29.2  35.7  0.0221 

800  30.3  36.8  0.0215 

1600  31.2  38.3  0.0226 

Table  XIV . — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
50  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  ^5°. 

Temperature 
V.  /iz/25°.  jWz/35°.  coefficients. 

10        7.34        9.94        0.0350 

50  8.44  11.41  0.0353 

ioo        8.86       11.98        0.0352 

200  9.21  12.48  0.0355 

400  9.49  12.87  0.0356 

800  9.59  13.05  0.0361 

1600  9.90  13-44  0.0357 

Table  XV. — Conductivity  of  Lithium  Bromide  in  a  Mixture  of 
75  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  55°. 

Temperature 
V.  A*f25°.  A*z/35°.  coefficients. 

10  1.73  2.78  0.0607 

50  2.01  3-21  0.0599 

ioo  2.13  3.38  0.0584 

200  2.30  3.38  0.0470 

400 

800  2.20  3.55  0.0614 

1600  2.17  3-49  0.0626 

Table   XVI. — Conductivity   of   Cobalt   Chloride   in   Glycerol   at 
25°,  35°,  and  45°- 

Temperature 
coefficients. 


V. 

fJ.v25°. 

Mz/35°. 

Atv45°. 

25°-35°. 

35°-45°. 

10 

0.27O 

0.546 

1.003 

0.1023 

0.0836 

50 

0.369 

0-744 

1-373 

O.IOI5 

o  .  0846 

IOO 

0.391 

0.784 

1.450 

o.  1004 

o  .  0780 

200 

0-455 

0.9II 

1.691 

o  .  1004 

0.0857 

400 

0-473 

0-959 

1.779 

o.  1027 

0.0855 

800 

0.497 

1.005 

1.856 

0.  IOII 

0.0847 

1600 

0.519 

I.O40 

1.920 

O.  IOO2 

o  .  0846 

38 

Table  XVII. — Conductivity  of  Cobalt  Chloride  in  Water  at  25° 

and  55°. 

Temperature. 
V.  /J,v25°.  fJ.v35°.  coefficients. 

10  168.9  204.7  0.0212 

50       195-5       236.8       0.0212 
ioo       204.2       246.7       0.0205 

200  212.6  256.5  0.0207 
4OO  219.4  267.9  O.O2I7 
800  226.6  276.9  0.0222 

1600  232.6  282.6  0.0216 

Table  XVIII. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
25  per  cent  Glycerol  and  Water  at  25°  and  55°. 


Temperature 

V. 

Hv25°. 

Mz/35°. 

coefficients. 

10 

79-9 

IOO.  I 

0.0252 

50 

92.6 

116.4 

0.0258 

IOO 

97.6 

122.9 

0.0259 

200 

101.7 

128.4 

0.0262 

400 

105.3 

I33-I 

0.0264 

800 

108.5 

136.6 

0.0260 

1600  i 10. 2  139-7  0.0267 

Table  XIX. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
50  per  cent  Glycerol  and  Water  at  25°  and  55°. 


Temperature 

V. 

/*z/25  °. 

Hv35°. 

coefficients. 

10 

28.8 

38-7 

o  .  0346 

50 

33-7 

45-4 

o  .  0346 

IOO 

35-4 

47.6 

0.0346 

20O 

37-i 

49-7 

o  .  0340 

400 

38-1 

51-2 

0.0344 

800 

39-4 

53-3 

0.0352 

I6OO 

40.4 

54-57 

0.0349 

Table  XX. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
75  per  cent  Glycerol  and  Water  at  25°  and  35°. 

Temperature 


V. 

Mz/25  °. 

Hv35°. 

coefficients. 

10 

5-72 

8.82 

0.0542 

50 

6-93 

10.64 

0.0536 

IOO 

7-30 

11.22 

0.0536 

200 

7.69 

11.87 

0.0543 

400 

7-94 

12.22 

0.0540 

800 

8.42 

12-95 

0.0538 

1600 

8-33 

12-75 

0.0531 

39 

Table  XXL — Conductivity  of  Cobalt  Chloride  in  Ethyl  Alcohol 
at  25°  and  35 ( 


V. 

Mz/25°. 

Atz/35  °. 

Temperature 
coefficients. 

10 

4.71 

4.96 

0.0053 

50 

IOO 

9.19 
I2.I8 

9-05 
II  .92 

O.OOI7 
O  .  OO2  I 

200 
400 
800 

I5-7I 
I9-56 
24.07 

15-54 
19.64 
24.91 

O.OOII 

o  .  0004 

0.0034 

i6oo  28.78  30.38  0.0056 

Table  XXII. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
25  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  /*z/25°.  pv35°.  coefficients. 

10  5.43  6.70  0.0233 

50  8.13  10.10  0.0243 

loo  9.30  11.52  0.0239 

200  10.66  13-25  0.0243 

400          12.14          15.01  0.0236 

800          13-89          17.28  0.0244 

1600          15.55          19.39  0.0246 

Table  XXIII. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
50  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  Hv25°.  pv35°.  coefficients. 

10  2.63  3.77  0.0436 

50  3-65  5-11  0.0400 

loo  4.12  5.78  0.0402 

200  4.66  6.53  0.0403 

400  5.14  7.32  0.0424 

800  5.65  8.03  0.0423 

1600  5-86  8.46  0.0443 

Table  XXIV. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
75  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  flv25°.  fAv35°.  coefficients. 

10  0.953  I-58  0.0652 


50 
IOO 
200 

400 

800 

1600 


29  2. I I  0.0638 

.41  2.32  0.0650 

.58  2.63  0.0662 

.69  2. 8 i  0.0666 

.89  3.14  0.0660 

.89  3-20  0.0662 


40 

Table  XXV.— Conductivity  of  Cobalt  Chloride  in  Methyl  Alcohol 
at  25°  and  35°. 

Temperature 
V.  /*z/25°.  /*z/35°.  coefficients. 

10  4L9  44-7  0.0066 

50  64.6  69.6  0.0077 

loo  75.6  82.5  0.0098 

200  88.9  94.6  0.0065 

400  102.2  II0.4  0.0080 

800  IlS.I  126.8  0.0078 

1600  132.5  144.6  0.0092 

Table  XXVI. — Conductivity  of  Cobalt  Chloride  in  a  Mixture 
of  25  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  55°. 


Temperature 

V. 

/iz/25°. 

/**35°. 

coefficients. 

10 

19.6 

23.0 

0.0173 

50 

27.8 

32-6 

0.0172 

100 

32.1 

37-7 

0.0175 

2OO 

36.6 

43-i 

0.0176 

400 

40.7 

48.2 

0.0185 

800 

44.8 

53-4 

0.0192 

1600 

48.8 

57-4 

0.0179 

Table  XXVII. — Conductivity  of  Cobalt  Chloride  in  a  Mixture  of 
50  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  35°. 


Temperature 

V. 

Hv25°. 

^35°. 

coefficients. 

10 

7.64 

10.01 

0.0310 

50 

IO.22 

13.64 

0.0334 

IOO 

11.64 

15-37 

0.0323 

200 

12.84 

17.07 

0.0330 

400 

14.11 

18.77 

0.0330 

800 

14.99 

20.  17 

0.0346 

1600 

15.41 

20.88 

0-0355 

Table  XXVIII. — Conductivity  of  Cobalt  Chloride  in  a  Mixture 
°f  75  Per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  35°. 


Temperature 

V. 

^25°. 

Pv35°. 

coefficients. 

10 

1.90 

3-00 

0.0577 

50 

2-55 

3-99 

0.0569 

IOO 

2.81 

4-43 

0.0577 

200 

3.12 

4-95 

0.0589 

400 

3-55 

5.36 

o  .  0600 

800 

3-51 

5-63 

o  .  0606 

1600 

3-59 

5.76 

o  .  0606 

Table  XXIX. — Conductivity  of  Potassium  Iodide  in  Glycerol  at 
25°,  55°,  and  45°- 


Temperature 
coefficients. 

Temperature 
coefficients. 

V. 

Hv25°.              Hv35°.               piA5°.               25°-35°. 

35°-45°. 

10 

0. 

291 

0. 

607 

i 

.189 

0. 

1087 

0. 

0844 

50 

O 

326 

o 

.667 

i 

•275 

0. 

1045 

0 

,0912 

IOO 

o 

•  324 

o 

.670 

i 

•257 

0. 

1068 

O 

.0875 

200 

0 

334 

0 

.687 

i 

.284 

0. 

1056 

O 

.0870 

4OO 

0 

338 

o 

,686 

i 

.282 

0. 

1030 

0 

.0871 

800 

0 

346 

o 

.708 

i 

•325 

0. 

1048 

0 

,0871 

1600 

0, 

352 

0 

,717 

i 

.326 

0. 

1039 

O 

,0849 

Table  XXX. — Conductivity  of  Potassium  Iodide  in  Water  at 

25°  and  35°. 

Temperature 
V.  /J,v25°.  A*z/35°.  coefficients. 

10  125.6  I5o.^  0.0189 

50  I3I.6  I56-5  0.0189 

ioo       133.6       159.3       0.0192 

200  135.8  I62.I  0.0193 
400  I37.2  163.7  0.0193 
800  138.9  165.9  0.0194 

1600  140.0  J67-5  0.0196 

Table  XXXI. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  25  per  cent  Glycerol  and  Water  at  25°  and  55°. 

Temperature 
V.  Mi/25  °.  ^7,35°.  coefficients. 

10        61.5        76.6        0.0244 

50        64 . 3        80 . i        o . 0246 

ioo       65.4       81.7       0.0249 

200  66.9  83.4  0.0249 

400  67.0  83.9  0.0251 

800  68.1  85.2  0.0252 

1600  68.7  86.0  0.0252 

Table  XXXII. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  50  per  cent  Glycerol  and  Water  at  25°  and  35°. 

Temperature 
V.  fJ,v25°.  /izX35°.  coefficients. 

10        23.9        30.8        0.0289 

50  24.4  32.3  0.0327 

ioo       24.6        32.8       0.0333 

200  24.9  33.2  0.0332 

400  25.1  33.4  0.0336 

800  25.4  34.1  0.0340 

1600  25.5  34.5  0.0351 


42 

Table  XXXIII. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  75  per  cent  Glycerol  and  Water  at  25°  and  55°. 

Temperature 
V.  /*z/25°.  /Az/35°.  coefficients. 

10 

50 
100 
200 
400 
800 
1600 

Table  XXXIV. — Conductivity   of  Potassium  Iodide   in  Ethyl 


4-94 

7.66 

0.0552 

5-13 

7.98 

0.0555 

5-25 

8.18 

0.0559 

S-H 

8.01 

0.0559 

5-42 

8.50 

0.0569 

5.48 

8.56 

0.0563 

5-20 

8.02 

0.0545 

V. 

nvitvinv*  **i> 

"  J7       w*w  ."jj     • 
^35°. 

Temperature 
coefficients. 

10 

50 

100 

21  .6 

28.5 

31-9 

24.8 
32.7 
36.9 

0.0146 
0.0148 
0.0156 

200 

35-4 

41-5 

O.OI7I 

400 

37-9 

44-5 

0.0173 

800  40.8  48.1  0.0177 

1600  42.6  50.3  0.0179 

Table  XXXV. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  25  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  Hv25°.  IMV35°.  coefficients. 


10 

9-50 

12.27 

0.0291 

50 

n-35 

14.68 

0.0293 

100 

12.  12 

15-79 

o  .  0303 

200 

12.88 

16.87 

o  .  0309 

400 

13.40 

17-56 

0.0310 

800 

13-99 

18.33 

0.0310 

1600 

14.62 

18.70 

0.0278 

Table  XXXVI. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  50  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  55°. 

Temperature 
V.  pv2S°.  /As/350.  coefficients. 

10  3.87  5.67  0.0466 

50  4.31  6.31  0.0466 
100 

200  4.66  6.93  0.0484 

400  4.78  7.03  0.0470 

800        4-96        7-29        0.0471 
1600       4.98       7.28       0.0460 


43 

Table  XXXVII. — Conductivity  of  Potassium  Iodide  in  a  Mix- 
ture of  75  per  cent  Glycerol  and  Ethyl  Alcohol  at  25°  and  55°. 


Temperature 

V.                            £ 

it/25  °. 

/*z/35  °. 

coefficients. 

10 

•  19 

2.05 

0.0723 

50 

•  19 

2  .  II 

0.0770 

100 

•33 

2.28 

0.0717 

200 

•39 

2-37 

0.0707 

400 

.42 

2-43 

o  .  0709 

8oo 

.46 

2.51 

o  .  0709 

1600 

•49 

2.50 

o  .  0700 

Table  XXXVIII. — Conductivity  of  Potassium  Iodide  in  Methyl 
Alcohol  at  25°  and  55°. 

Temperature 


V. 

Hv25°. 

/iz/35°. 

coefficients. 

10 

65.5 

72.9 

O.OII4 

50 

79-6 

89.1 

0.0120 

100 

84.0 

94.1 

O.OI2I 

200 

90.9 

102.  I 

O.OI22 

4OO 

94.8 

106.6 

0.0125 

800 

98.0 

III.  2 

0.0134 

1600 

100.8 

113-4 

0.0125 

Table  XXXIX. — Conductivity  of  Potassium  Iodide  in  a  Mixture 
of  25  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  35°. 


Temperature 

V. 

/*z/25°. 

Hv3S°. 

coefficients. 

10 

26.4 

32.2 

O.O2I9 

50 

30.6 

37-3 

0.0220 

100 

31-8 

38.6 

0.0218 

200 

33-3 

40-5 

0.0217 

4OO 

34-2 

41.9 

0.0224 

800 

35-3 

43-o 

0.0218 

I60O 

35-7 

44.1 

0.0233 

Table  XL.  —  Conductivity  of  Potassium  Iodide  in  a  Mixture  of 
50  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  55°. 

Temperature 
V.  /w^25°.  /U7/350.  coefficients. 


10  9.15  12.5  0.0366 

50  10.2  13.9  0.0365 

loo  10.4  14.2  0.0363 

200  10.8  14.8  0.0364 

400  II.  I  15.1  0.0363 

800  II.5  15.6  0.0364 

1600  i  i.  8  16.1*  0.0364 


44 

Table  XLI. — Conductivity  of  Potassium  Iodide  in  a  Mixture  of 
75  per  cent  Glycerol  and  Methyl  Alcohol  at  25°  and  35°. 

Temperature 
V.  /*t>25°.  pv3S°.  coefficients. 

10       2.08       3.41        0.0635 

50  2.28  3.68  0.0619 

ioo       2.39       3.90       0.0635 

200  2.35  3.82  0.0624 

400  2.40  3.90  0.0631 

800  2.56  4.27  0.0663 

1600  2 . 46  4 . 07  o . 0648 


,  Tables  IV.  to  XV.  show  the  conductivities  of  lithium  bromide 
in  various  mixtures  of  glycerol  with  water,  methyl  alcohol, 
and  ethyl  alcohol.  The  results  are  plotted  in  Figures  I.,  II., 
and  III.  The  curves  show  that  the  conductivities  in  the  mix- 
tures depart  widely  from  the  law  of  averages,  there  being 
a  marked  sagging  of  the  curves  in  each  case.  The  results 
are  much  like  those  obtained  by  Jones  and  Carroll  with  cad- 
mium iodide  in  mixtures  of  water  and  methyl  alcohol.  No 
minimum  is  observed,  nor,  indeed,  has  any  minimum  appeared 
in  all  the  work  with  glycerol  solutions.  This  is  not  surprising. 
It  is  hardly  probable  that  any  mixture  of  glycerol  with  the 
less  viscous  solvents  would  have  a  viscosity  greater  than  that 
of  pure  glycerol.  It  is  conceivable,  however,  that  a  mix- 
ture of  glycerol  with  a  very  small  percentage  of  water  or 
alcohol  might  give  a  slight  minimum  in  fluidity,  but  the  diffi- 
culty of  determining  this  point  would  be  very  great.  At 
the  same  time,  a  similar  minimum  in  the  conductivity  curves 
might  make  its  appearance,  and  the  parallelism  of  the  two 
sets  of  curves,  which  is  one  of  the  points  to  be  established, 
would  not  be  changed,  even  if  minima  were  found.  At  any 
rate,  it  is  evident  that  in  the  case  of  mixtures  of  glycerol 
with  the  other  three  solvents  used,  we  have  to  deal  with  mix- 
tures of  the  second  class  referred  to  above;  that  is,  mixtures 
whose  properties  are  not  additive. 


45 


25  50  75 

Per  cent  Glycerol. 
'Fig.  I. — Conductivity  of  Lithium  Bromide  in  Glycerol-Water  at  25°. 


Cobalt  Chloride. 

The  cobalt  chloride  was  first  crystallized  from  conductivity 
water,  to  free  it  from  traces  of  sulphates.  The  crystalliza- 
tion was  continued  until  the  mother  liquor  no  longer  clouded 
barium  chloride  solution.  The  salt  was  then  partially  de- 
hydrated in  a  vacuum  desiccator,  with  sulphuric  acid,  after 
which  it  was  pulverized,  and  heated  in  the  air  till  it  had  as- 
sumed a  lavender  color.  After  being  again  pulverized,  it 


46 


25  50  75 

Per  cent  Glycerol 
Fig.  II. — Conductivity  of  Lithium  Bromide  in  Glycerol-Ethyl  Alcohol  at  25°. 


47 


o  25  50  75 

Per  cent  Glycerol. 
Fig.  III. — Conductivity  of  Lithium  Bromide  in  Glycerol-Methyl  Alcohol  at  25°. 


48 

was  placed  in  a  hard-glass  tube,  and  heated  in  a  current  of 
dry  hydrochloric  acid  gas  for  several  hours  at  250°,  during 
which  process  it  changed  color  to  a  pale  pure  blue.  The 
hydrochloric  acid  gas  was  then  replaced  by  a  stream  of  nitrogen 
dried  over  phosphorus  pentoxide,  and  the  tube  allowed  to 
cool  slowly.  The  cobalt  chloride  gave  a  clear  solution  in 
water,  which,  however,  when  exposed  to  sunlight,  deposited 
a  very  small  quantity  of  a  flocculent  brown  precipitate.  Not 
enough  of  this  could  be  obtained  for  a  complete  examination. 
It  did  not  contain  iron,  and  did  not  give  the  reactions  of 
bivalent  cobalt.  It  is  thought  to  be  a  cobaltic  compound, 
produced  by  some  oxidizing  action  brought  about  by  the  sun- 
light. Solutions  kept  in  the  dark  did  not  show  this  precipitate, 
even  when  allowed  to  stand  overnight;  but  ten  minutes' 
exposure  to  bright  sunlight  was  sufficient  to  cause  the  change. 
For  this  reason,  the  conductivities  of  cobalt  chloride  in  aqueous 
solution  are  considered  a  little  uncertain,  and  are  probably 
a  little  too  high.  Solutions  in  the  alcohols  and  in  glycerol 
were  perfectly  clear,  and  remained  so  indefinitely,  sunlight 
having  no  effect  on  them. 

The  conductivities  of  cobalt  chloride  are  given  in  Tables 
XVI.  to  XXVIII.  The  conductivities  in  pure  glycerol  in- 
crease regularly,  and  are  considerably  higher  than  the  corre- 
sponding values  for  lithium  bromide.  This  is  just  what  would 
be  expected,  if  glycerol  is  a  normal  dissociating  solvent.  Cobalt 
chloride  would  dissociate  into  three  ions,  while  lithium  bromide 
would  give  only  two,  and  the  conductivities  of  the  former 
salt  would  accordingly  be  greater. 

The  results  are  plotted  as  curves  in  Figures  IV.,  V.,  and  VI. 
The  curves  are  in  every  respect  analogous  to  those  for  lithium 
bromide,  except  in  one  minor  point,  to  be  seen  in  Figure  V. 
Here  the  values  of  conductivity  of  cobalt  chloride  in  pure 
ethyl  alcohol  are  abnormally  low  (at  least  for  all  except  the 
most  dilute  solutions),  considering  it  is  a  ternary  electrolyte. 
Lithium  bromide,  for  instance,  in  the  tenth-normal  solution 
in  ethyl  alcohol,  has  a  molecular  conductivity  of  15.8  at  25°, 
and  we  should  expect,  other  things  being  equal,  that  cobalt 
chloride  would  give  a  value  about  50  per  cent  greater  than 


49 


50  75  ioo 

Per  cent  Glycerol. 
Fig.  IV. — Conductivity  of  Cobalt  Chloride  in  Glycerol-Water  at  25°. 

this.  The  value  of  ^25°  for  cobalt  chloride  in  ethyl  alcohol 
is,  however,  only  4.71.  But  knowing  that  many  of  the  halides 
of  the  heavy  metals  tend  to  form  complexes  when  dissolved 
in  organic  solvents,  it  was  suspected  that  these  low  results, 
at  least  in  the  concentrated  solutions,  were  due  to  partial 
polymerization  of  the  cobalt  chloride  molecules.  This  point 
was  kindly  tested  for  us  by  Mr.  H.  R.  Kreider.  He  showed 
by  the  boiling  point  method  that  the  dissociation  of  cobalt 
chloride  in  ethyl  alcohol,  for  concentrations  ranging  near 


75 


^5  50 

Per  cent  Glycerol. 
Fig.  V. — Conductivity  of  Cobalt  Chloride  in  Glycerol-Ethyl  Alcohol  at  25°. 


100 


150 


o  25  50 

Per  cent  Glycerol. 
Fig.  VI. — Conductivity  of  Cobalt  Chloride  in  Glycerol-Methyl;Alcohol  at  25 


100 


52 

tenth-normal,  is  apparently  negative;  or,  in  other  words, 
the  indicated  molecular  weight  is  greater  than  that  calculated 
for  CoCl2.  Some  of  his  results  are  given  here. 

M.  W.  =  129.96. 

Volume.  M.  W.  found. 

8-1  155 

i3-o  134 

13-3  131 

The  association  appears  in  all  three  solutions,  and  since 
most  other  salts  are  dissociated  20  to  30  per  cent  in  ethyl 
alcohol  at  these  concentrations,  we  may  consider  the  low  con- 
ductivity of  cobalt  chloride  in  this  case  to  be  due  to  this  cause. 
The  same  thing  is  shown  in  methyl  alcohol  solutions.  The 
value  of  /V25°  for  lithium  bromide  in  tenth-normal  solution 
is  50.0,  against  a  corresponding  value  of  41.9  for  cobalt  chloride. 
The  difference  is  not  so  striking  here,  probably  because  methyl 
alcohol  is  a  stronger  dissociant  than  ethyl  alcohol. 

Potassium  Iodide. 

Kahlbaum's  pure  potassium  iodide  was  recrystallized, 
and  dried  to  constant  weight  at  150°.  It  showed  no  appre- 
ciable impurity. 

Tables  XXIX.  to  XU.  give  the  conductivities  of  potassium 
iodide  in  glycerol,  and  in  the  mixed  solvents.  Again,  the 
conductivities  increase  nearly  regularly  with  dilution,  and 
are  a  little  higher  than  those  of  lithium  bromide,  and  about 
50  per  cent  less  than  the  conductivities  of  cobalt  chloride, 
as  we  should  expect.  The  results  in  the  mixtures  are  repre- 
sented in  Figures  VII.,  VIII.,  and  IX.,  and  are  in  every  respect 
like  those  obtained  for  the  other  two  salts.  The  conductivities 
are  less  than  the  averages  in  each  case. 


53 


zoo- 


50- 


o  as  50  75 

Per  cent  Glycerol. 
Fig.  VII. — Conductivity  of  Potassium  Iodide  in  Glycerol-Water  at  25°. 


too 


54 


o  25  50  75  ioo 

Per  cent  Glycerol. 
Fig.  VIII.— Conductivity  of  Potassium  Iodide  in  Glycerol-Ethyl  Alcohol  at  25°. 


55 


o  25  50 

Per  cent  Glycerol. 
Fig.  IX. — Conductivity  of  Potassium  Iodide  in  Glycerol-Methyl  Alcohol  at  25°. 


56 

Temperature  Coefficients  of  Conductivity. 

The  most  interesting  features  in  this  connection  are  the 
very  large  temperature  coefficients  of  conductivity  of  the  solu- 
tions in  pure  glycerol.  In  tenth-normal  solution,  these  are 
for  lithium  bromide,  cobalt  chloride,  and  potassium  iodide, 
respectively,  10.6  per  cent,  10.23  per  cent  and  10.87  Per  cent 
between  25°  and  35°,  and  8.71  per  cent,  8.36  per  cent,  and 
8.44  per  cent  between  35°  and  45°.  These  are  much  the 
largest  temperature  coefficients  of  conductivity  thus  far  observed 
between  these  temperatures,  and  they  are  closely  related  to  the 
temperature  coefficients  of  fluidity. 

In  the  solutions  of  cobalt  chloride  in  ethyl  alcohol,  nega- 
tive temperature  coefficients  of  conductivity  occur.  These 
have  also  been  noticed  by  Jones  and  McMaster  in  certain 
solutions  of  the  same  salt  in  mixtures  of  acetone  and  the  alco- 
hols. In  the  present  case,  the  temperature  coefficient  of  the 
tenth-normal  solution  is  positive,  though  very  small,  and 
in  the  fiftieth-normal  solution  it  becomes  negative.  The 
temperature  coefficients  reach  a  minimum  in  the  hundredth- 
normal  solution,  and  then  increase  regularly,  again  becoming 
positive  in  the  dilute  solutions.  Temperature  coefficients  of 
conductivity  in  ethyl  alcohol  are  always  small,  and  it  is  known 
that  the  degree  of  ionization  decreases  with  rising  temperature. 
We  have  already  proved  that  cobalt  chloride  in  ethyl  alcohol 
has  a  strong  tendency  to  polymerize.  The  occurrence  of 
negative  temperature  coefficients  of  conductivity,  therefore, 
shows  that  the  decrease  in  ionization,  due  to  rise  in  tem- 
perature, is  more  than  sufficient  to  overcome  the  effect  of 
increased  ion  velocity,  brought  about  by  increased  fluidity. 

In  the  mixed  solvents,  the  temperature  coefficients  of  con- 
ductivity in  no  case  follow  the  law  of  averages,  but,  like  the 
conductivities,  are  always  less  than  the  calculated  values. 

We  have  thus  shown  that  for  solutions  in  mixtures  of  glycerol 
with  water  or  the  alcohols,  the  molecular  conductivities  are 
always  less  than  the  averages  calculated  from  the  conduc- 
tivities in  the  component  solvents.  Hence,  we  may  conclude 
that  glycerol  is  a  solvent  which,  when  mixed  with  another, 


57 


gives  a  mixture  whose  properties  are  not  additive,  and  in 
this  respect  glycerol  resembles  water.  In  the  three  cases 
tested,  glycerol  causes  some  change  in  the  state  of  molecular 
aggregation  of  the  other  solvents,  producing  mixtures  similar, 
in  many  ways,  to  mixtures  of  water  with  the  alcohols  or  ace- 
tone. We  can  now  proceed  to  show  that  the  departure  from 
the  law  of  averages  is  just  as  pronounced  when  we  examine 
the  fluidities  of  the  mixtures  of  glycerol. 


Table  XLII 


Solution. 

LiBr 
CoCl2 
KI 
Solvent 


LiBr 
CoCl2 
KI 
Solvent 


LiBr 
CoCl2 
KI 
Solvent 


— Viscosity  and  Fluidity  of  Solutions  in  Mixtures 
of  Glycerol  and  Water  at  25°  and  55°. 
Water. 

T)  25.        T)  35.  <f>  25.       0  35.  T.  C.  0. 

O.OOQOII  0.00723  110-99  138.33  0.0246 

0.009209  0.00745  108.58  134.26  0.0237 

0.008847  0.007I9I  113.02  139.06  0.0231 

0.00891       0.00720       112.25     J38.S9     0.0237 
25  Per  Cent  Glycerol  and  Water. 

0.02064  0.01552  48-45  64 -44  0.0330 

0.02156  0.01624  46.49  61.65  0.0326 

0.01991  0.01509  50.23  66.25  0.0319 

0.02003  0.01518  49.91  "65.86  0.0319 

50  Per  cent  Glycerol  and  Water. 

0.06246  0.04346  16.01  23.01  0.0437 

0.06659  0.04632  15.02  21.59  0.0438 

0.06060  0.04252  16.50  23.52  0.0425 

0.06145  0.04272  16.27  23.41  0.0438 

75  Per  cent  Glycerol  and  Water. 

3.003  4.949  0.0647 

2.743  4-541  0.0656 

3.081  5.046  0.0638 

3.122  5.118  0.0639 


Table  XLIII. — Viscosity  and  Fluidity  of  Solutions  in  Mixtures 

of  Glycerol  and  Ethyl  Alcohol  at  25°  and  55°. 

Ethyl  Alcohol. 


LiBr 

0.3330 

0.2020 

CoCl2 

0-3645 

0.2202 

KI 

0.3246 

o.  1982 

Solvent 

0.3203 

0.1954 

Solution. 

,25. 

T)  35. 

025. 

035. 

T.  C.  0. 

LiBr 

o. 

01235 

0. 

009864 

80 

.92 

101  . 

37 

0. 

0253 

CoCl2 

O, 

OII93 

0 

009828 

83 

.80 

101. 

75 

0 

0214 

KI 

0. 

OII77 

0. 

00960 

84 

•95 

104, 

16 

O 

0226 

Solvent 

0. 

OHIO 

o 

009068 

90 

.07 

HO. 

28 

0. 

0224 

2 5  Per  cent  Glycerol  and  Ethyl  Alcohol. 

LiBr         0.04574     0.03305       21.86       30.26  0.0384 

CoCl2        0.04919     0.03612       20.33       27.69  0.0362 

KI  0.0452       0.03290       22.12       30.39  0.0374 

Solvent    0.04367     0.03188       22.90       31.37  0.0370 

50  Per  cent  Glycerol  and  Ethyl  Alcohol. 

LiBr         0.2275       0.1413  4-5I5       7-075  0.0588 

CoCl2        0.2449       0.1569  4.084       6.375  0.0561 

KI  0.2059       0.1327  4-856       7-537  0.0552 

Solvent    0.2053       0.1323  4.871       7.559  0.0552 

75  Per  cent  Glycerol  and  Ethyl  Alcohol. 

LiBr         1.193         0.6455  0.8382     1.549  0.0848 

CoCl2        1.353         0.7381  0.7391     1.355  0.0833 

KI  1.1005       0.6038  0.9089     1.656  0.0822 

Solvent    1.0842       0.5971  0.9223     1.675  0.0816 


Table  XLIV. — Viscosity  and  Fluidity  of  Solutions  in  Mixtures 
of  Glycerol  and  Methyl  Alcohol  at  25°  and  55°. 
Methyl  Alcohol. 


Solution. 

$25. 

?  35. 

025. 

035. 

T. 

C.  0. 

LiBr 

o 

,  006097 

0, 

005305 

164 

.01 

188 

•52 

0. 

0149 

CoCl2 

0 

006365 

0, 

005404 

157 

.  10 

181 

-65 

0. 

0135 

KI 

0 

005942 

o, 

005H9 

168 

•  31 

194 

.21 

O. 

0154 

Solvent 

o 

.005654 

0. 

004918 

176 

.86 

204 

•59 

0. 

0149 

25  Per  cent  Glycerol  and  Methyl  Alcohol. 

LiBr  0.02105  0.01647  47.51  60.72 

CoCl2  0.02247  0.01735  44. 5 1  57-64 

KI  0.02019  0.01588  49.52  62.98 

Solvent  0.01962  0.01539  50.97  64.97 

50  Per  cent  Glycerol  and  Methyl  Alcohol. 

LiBr  0.1012  0.06945  9.882  14.40 

CoCl2  0.1080  0.07451  9.258  13.42 

KI  0.0936  0.06353  10.68  15.54 

Solvent  0.0928  0.06379  10.78  15.68 

75  Per  cent  Glycerol  and  Methyl  Alcohol. 

LiBr  0.6525  0.3803  1-532  2.630 

CoCl2  0.7379  0.4165  1.352  2.401 

KI  0.6288  0.3637  1-590  2.750 

Solvent  0.6073  0.3552  1-647  2.815 


0.0279 
0.0295 
0.0272 
0.0274 


0.0458 
o . 0450 
0.0474 


0.0454 


0.0717 
0.0776 
0.0729 
o . 0709 


59 

Table  XLV. — Viscosity  and  Fluidity  of  Solutions  in  Glycerol 
'  at  25°  and  35°. 

Solution.  fj  25.  fj  35.  0  25.  (j>  35.  T.  C.  <f>. 

LiBr  6.786  3.192  0.1474  0.3133  0.1126 

CoCl2  7-530  3-364  0.1328  0.2973  0.1261 

KI  6.723  3-J39  0.1487  0.3186  0.1143 

Solvent  6.330  2.9403  0.1580  0.3401  0.1153 

Viscosity  and  Fluidity. 

Tables  XUI.  to  XLV.,  inclusive,  give  the  viscosities  and 
fluidities  of  the  pure  solvents,  the  mixed  solvents,  and  the 
tenth-normal  solutions  of  the  three  salts  in  these  liquids. 
The  fluidities  of  the  solutions  are,  as  usual,  in  nearly  every 
case  less  than  those  of  the  corresponding  solvents.  In  three 
solutions,  however,  we  have  the  phenomenon  of  negative 
viscosity.  These  are  potassium  iodide  in  water,  and  in  25 
and  50  per  cent  glycerol  and  water,  at  both  25°  and  35°. 
An  explanation  of  negative  viscosity  has  been  given  by  Jones 
and  Veazey.1  It  is  interesting  to  find  that  the  fluidity  of 
even  so  immobile  a  liquid  as  50  per  cent  glycerol  and  water 
is  increased  by  the  addition  of  potassium  iodide.  In  the 
75  per  cent  mixture,  the  viscosity  coefficient  is  again  positive, 
but  the  difference  between  the  viscosity  of  the  mixture  and 
of  tenth-normal  potassium  iodide  in  it  is  not  great.  The  salt 
does  not  lower  the  viscosity  of  pure  glycerol,  nor  of  any  of 
the  other  solvents  used. 

But  if  we  examine  the  viscosities  of  the  solutions  in  pure 
glycerol,  we  see  that  the  effect  of  the  several  salts  on  the  vis- 
cosity of  the  solvent  is  in  inverse  ratio  to  the  molecular  vol- 
umes of  the  salts.  Potassium  iodide,  with  the  largest  molecular 
volume,  increases  the  viscosity  of  glycerol  less  than  does 
lithium  bromide,  which  has  a  slightly  smaller  molecular  vol- 
ume. The  latter  salt,  in  turn,  increases  the  viscosity  of  glycerol 
much  less  than  does  cobalt  chloride,  which  has  much  the 
smallest  molecular  volume  of  the  three.  Relations  exactly 
analogous  to  these  have  been  pointed  out  by  Jones  and  Veazey, 
and  the  mechanism  of  the  effect  has  been  sufficiently  discussed 
in  the  first  part  of  this  work. 

1  Am.  Chem.  Journ.,  37,  405  (1907). 


6o 

The  viscosity  of  pure  glycerol  at  25° — 6.330 — is  1120  times 
that  of  methyl  alcohol  at  the  same  temperature.  A  wide 
range  of  viscosity  has  thus  been  covered,  yet  the  same  rela- 
tions hold  as  obtain  in  mixtures  of  the  much  more  fluid  sol- 
vents studied  by  Jones  and  his  co workers  The  fluidities  at 
25°  are  plotted  as  curves  in  Fig.  X.  Curve  I.  represents 
the  fluidities  of  glycerol- methyl  alcohol  mixtures,  curve  II. 
represents  glycerol- water,  and  curve  III.  represents  glycerol- 
ethyl  alcohol.  The  curves  resemble  the  conductivity  curves 
very  closely,  show  the  same  sagging,  and  have  no  minima. 

The  temperature  coefficient  of  fluidity  of  pure  glycerol 
between  25°  and  35°  is  11.53  Per  cent,  and  this  is  very  nearly 
equal  to  the  temperature  coefficients  of  conductivity  of  the 
salts  used  in  this  work.  In  all  the  solutions,  the  temperature 
coefficient  of  fluidity  is  greater  than  the  temperature  co- 
efficients of  conductivity,  as  has  been  observed  in  practically 
all  cases  heretofore.  This  is  probably  due  partly  to  the  de- 
crease of  dissociation  with  rising  temperature. 

It  will  be  seen  that  in  the  majority  of  cases,  the  tempera- 
ture coefficient  of  fluidity  of  any  solution  is  slightly  greater 
than  that  of  the  solvent.  As  is  known,  dissociation  decreases 
slightly  with  rising  temperature.  This  would  cause  the  solu- 
tion at  higher  temperature  to  contain  a  greater  number  of 
whole  molecules,  whose  volume  would  be  equal  to  that  of  their 
component  ions,  but  whose  frictional  surfaces  would  be  less. 
This  would  decrease  the  total  frictional  surface  of  the  particles 
in  the  solution,  and  an  increase  in  the  fluidity  would  result, 
in  addition  to  that  caused  by  the  ordinary  increase  in  the 
fluidity  of  the  pure  solvent.  This  relation  does  not  hold  for 
all  of  the  temperature  coefficients  of  fluidity,  but  the  excep- 
tions are  not  many,  and  it  would  seem  that  an  explanation 
like  the  above  is  at  least  partially  correct. 

A  comparison  of  the  conductivity  and  fluidity  curves  shows, 
then,  that  the  two  phenomena,  in  mixtures  of  glycerol  with 
water  or  the  alcohols,  are  very  closely  parallel.  No  minima 
are  found,  but  every  curve  shows  a  falling  below  the  straight 
line  of  averages.  Hence,  we  must  conclude  that  glycerol 
is  a  solvent  resembling  water  more  closely  than  it  does  the 


50  75 

Per  cent  Glycerol. 
Fig.  X. — Fluidities  of  Glycerol  Mixtures  at  25°. 


62 

alcohols,  in  that  mixtures  containing  it  do  not  have  additive 
properties.  This  resemblance  to  water  comes  out  more  strik- 
ingly when  we  examine  the  relative  values  of  the  conduc- 
tivities of  the  three  salts  studied  here,  in  the  different  pure 
solvents.  In  water,  cobalt  chloride,  being  a  ternary  elec- 
trolyte, has  a  greater  conductivity  than  potassium  iodide, 
and  potassium  iodide  again  has  a  conductivity  greater  than 
lithium  bromide.  The  same  order  is  found  in  glycerol.  In 
ethyl  alcohol,  and  in  the  tenth-normal  solutions  in  methyl 
alcohol,  the  order  is  potassium  iodide,  lithium  bromide,  co- 
balt chloride.  We  have  already  shown  that  cobalt  chloride 
in  ethyl  alcohol  forms  complexes.  It  is  evident  that  in  glycerol 
the  same  salt  does  not  form  complexes,  but  behaves  like  a 
normal  ternary  electrolyte  in  a  strongly  dissociating  solvent. 
It  seems  to  be  broken  down,  at  least  partly,  into  three  ions, 
even  in  the  fairly  concentrated  solutions  in  glycerol,  and  in 
this  point  the  latter  resembles  water  rather  than  the  alcohols. 

The  conductivities  of  the  several  electrolytes  in  pure  glycerol 
do  not  reach  limiting  values  in  the  dilutions  worked  with 
here,  but  the  conductivities  for  dilutions  of  four-hundredth- 
normal  and  more  are  increasing  very  slowly;  in  other 
words,  complete  dissociation  is  probably  reached  in  glycerol 
solutions  at  a  comparatively  small  volume.  This  feature 
again  recalls  the  dissociating  action  of  water. 

If  we  multiply  0.35,  the  highest  conductivity  obtained 
for  potassium  iodide  in  glycerol  at  25°,  by  6.330,  the  viscosity 
of  the  solvent  at  that  temperature,  the  product  is  2.22.  Simi- 
larly, at  35°  the  product  is  2.10.  These  numbers,  nearly 
identical,  represent  lower  limits,  so  to  speak  of  the  product 
H^  f)  for  glycerol.  It  will  be  recalled  that  Walden  found  this 
value  to  be  nearly  a  constant,  independent  of  temperature, 
for  about  thirty  organic  solvents.  Water  and  glycol,  with 
values  equal  to  i.o  and  1.32  respectively,  were  exceptions. 
Glycerol  thus  becomes  another  exception,  with  a  product  of 
at  least  2.10.  If  we  compare  methyl  alcohol,  the  simplest 
monacid  carbinol,  with  glycerol,  the  simplest  diacid  carbinol, 
and  with  glycerol,  the  simplest  triacid  carbinol,  we  see  that 


63 

conductivity   does   not   increase   proportionately    to   fluidity, 
but  to  some  fractional  power  of  fluidity. 


Solvent. 

CH3OH  0.72 

C2H4(OH)2  1.32 

C3H5(OH)3  2.10 

A  similar  conclusion  has  been  drawn  by  Green1  from  a  study 
of  the  conductivity  and  viscosity  of  solutions  of  lithium  chlor- 
ide in  water  containing  various  amounts  of  sucrose,  and 
he  finds  that 


Summary  of  Facts  Established. 

(1)  Glycerol,  with  water,  or  with  methyl  or  ethyl  alcohol, 
forms  binary  mixtures  whose  properties  are  not  additive. 

(2)  The  conductivity  curves  of  three  electrolytes  in  these 
mixtures  in  no  case  obey  the  law  of  averages. 

(3)  The  same  is  true  of  the  fluidity  curves. 

(4)  The  temperature  coefficients  of  conductivity  of  solutions 
in  pure  glycerol  are  very  large,  and  nearly  identical  with  the 
temperature  coefficients  of  fluidity. 

(5)  Glycerol,  as  a  dissociating  liquid,  resembles  water  more 
closely  than  it  does  the  alcohols. 

(6)  Conductivity    increases   with    fluidity,    but   instead    of 
increasing  at  the  same  rate,  varies  as  some  fractional  power 
of  fluidity. 

i  J.  Chem.  Soc.,  93,  2049  (1908). 


BIOGRAPHY. 

Maurice  Roland  Schmidt,  the  author  of  this  dissertation, 
was  born  in  Baltimore,  Md.,  December  3,  1885.  His  primary 
education  was  received  in  the  public  schools  of  that  city.  In 
1898  he  entered  the  Baltimore  City  College,  and  graduated  in 
1903.  In  the  fall  of  the  same  year,  he  entered  the  under- 
graduate department  of  Johns  Hopkins  University,  and  re- 
ceived the  Bachelor's  degree  in  1906.  He  continued  his 
studies  in  chemistry  at  the  same  institution,  with  physical 
chemistry  and  geology  as  subordinate  subjects.  During  the 
years  1906—1907  and  1907—1908  he  was  student  assistant  in 
chemistry  at  Johns  Hopkins,  and  in  1908  was  appointed  Fellow 
in  chemistry. 


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